Receiving apparatus and de-interleaving method thereof

ABSTRACT

A transmitting apparatus and a receiving apparatus are provided. The transmitting apparatus includes: an encoder configured to generate a low density parity check (LDPC) codeword by LDPC encoding based on a parity check matrix; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the modulator is further configured to map a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.

CROSS-REFERENCE TO THE RELATED APPLICATIONS

This is a continuation of U.S. patent application Ser. No. 16/505,226,filed on Jul. 8, 2019, which is a continuation of U.S. patentapplication Ser. No. 16/042,628, filed on Jul. 23, 2018, issued as U.S.Pat. No. 10,382,063 on Aug. 13, 2019, which is a continuation of U.S.patent application Ser. No. 15/435,042, filed on Feb. 16, 2017, issuedas U.S. Pat. No. 10,033,409 on Jul. 24, 2018, which is a continuation ofU.S. patent application Ser. No. 15/130,204, filed on Apr. 15, 2016,issued as U.S. Pat. No. 9,692,454 on Jun. 27, 2017, which is acontinuation of U.S. patent application Ser. No. 14/625,862, filed onFeb. 19, 2015, issued as U.S. Pat. No. 9,602,137 on Mar. 21, 2017, whichclaims priority from U.S. Provisional Application 61/941,676 filed onFeb. 19, 2014, U.S. Provisional Application 62/001,170 filed on May 21,2014, and Korean Patent Application 10-2015-0000671 filed on Jan. 5,2015. The entire disclosures of the prior applications are consideredpart of the disclosure of this continuation application, and are herebyincorporated by reference.

BACKGROUND 1. Technical Field

Apparatuses and methods consistent with exemplary embodiments relate toa transmitting apparatus and an interleaving method thereof, and moreparticularly, to a transmitting apparatus which processes data andtransmits the data, and an interleaving method thereof.

2. Description of the Related Art

In the 21st century information-oriented society, broadcastingcommunication services are moving into the era of digitalization,multi-channel, wideband, and high quality. In particular, as highquality digital televisions and portable multimedia player and portablebroadcasting equipments are increasingly used in recent years, there isan increasing demand for methods for supporting various receivingmethods of digital broadcasting services.

In order to meet such demand, standard groups are establishing variousstandards and are providing a variety of services to satisfy users'needs. Therefore, there is a need for a method for providing improvedservices to users with high decoding and receiving performance.

SUMMARY

Exemplary embodiments may overcome the above disadvantages and otherdisadvantages not described above. However, it is understood that theexemplary embodiment are not required to overcome the disadvantagesdescribed above, and may not overcome any of the problems describedabove.

The exemplary embodiments provide a transmitting apparatus which can mapa bit included in a predetermined bit group from among a plurality ofbit groups of a low density parity check (LDPC) codeword onto apredetermined bit of a modulation symbol, and transmit the bit, and aninterleaving method thereof.

According to an aspect of an exemplary embodiment, there is provided atransmitting apparatus which may include: an encoder configured togenerate an LDPC codeword by LDPC encoding based on a parity checkmatrix; an interleaver configured to interleave the LDPC codeword; and amodulator configured to map the interleaved LDPC codeword onto amodulation symbol, wherein the modulator is further configured to map abit included in a predetermined bit group from among a plurality of bitgroups constituting the LDPC codeword onto a predetermined bit of themodulation symbol.

Each of the plurality of bit groups may be formed of M number of bits,and M may be a common divisor of N_(ldpc), and K_(ldpc) and may bedetermined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) is acyclic shift parameter value regarding columns in a column group of aninformation word submatrix of the parity check matrix, N_(ldpc) is alength of the LDPC codeword, and K_(ldpc) is a length of informationword bits of the LDPC codeword.

The interleaver may include: a parity interleaver configured tointerleave parity bits of the LDPC codeword; a group interleaverconfigured to divide the parity-interleaved LDPC codeword by theplurality of bit groups and rearrange an order of the plurality of bitgroups in bit group wise; and a block interleaver configured tointerleave the plurality of bit groups the order of which is rearranged.

The group interleaver may be configured to rearrange the order of theplurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method isQPSK, and the code rate is 13/15, π(j) in Equation 21 may be defined asin Table 36.

The interleaver may include: a group interleaver configured to dividethe LDPC codeword into the plurality of bit groups and rearrange anorder of the plurality of bit groups in bit group wise; and a blockinterleaver configured to interleave the plurality of bit groups theorder of which is rearranged.

The group interleaver may be configured to rearrange the order of theplurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method isQPSK, and the code rate is 5/15, π(j) in Equation 21 is defined as inTable 32.

The block interleaver may be configured to interleave by writing theplurality of bit groups in each of a plurality of columns in bit groupwise in a column direction, and reading each row of the plurality ofcolumns in which the plurality of bit groups are written in bit groupwise in a row direction.

The block interleaver may be configured to serially write, in theplurality of columns, at least some bit groups which are writable in theplurality of columns in bit group wise from among the plurality of bitgroups, and then divide and write the other bit groups in an area whichremains after the at least some bit groups are written in the pluralityof columns in bit group wise.

According to an aspect of another exemplary embodiment, there isprovided an interleaving method of a transmitting apparatus. The methodmay include: generating an LDPC codeword by LDPC encoding based on aparity check matrix; interleaving the LDPC codeword; and mapping theinterleaved LDPC codeword onto a modulation symbol, wherein the mappingincludes mapping a bit included in a predetermined bit group from amonga plurality of bit groups constituting the LDPC codeword onto apredetermined bit of the modulation symbol.

Each of the plurality of bit groups may be formed of M number of bits,and M may be a common divisor of N_(ldpc), and K_(ldpc) and may bedetermined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) is acyclic shift parameter value regarding columns in a column group of aninformation word submatrix of the parity check matrix, N_(ldpc) is alength of the LDPC codeword, and K_(ldpc) is a length of informationword bits of the LDPC codeword.

The interleaving may include: interleaving parity bits of the LDPCcodeword; dividing the parity-interleaved LDPC codeword by the pluralityof bit groups and rearranging an order of the plurality of bit groups inbit group wise; and interleaving the plurality of bit groups the orderof which is rearranged.

The rearranging in bit group wise may include rearranging the order ofthe plurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method isQPSK, and the code rate is 13/15, π(j) in Equation 21 may be defined asin Table 36.

The interleaving may include: dividing the interleaved LDPC codewordinto the plurality of bit groups and rearranging an order of theplurality of bit groups in bit group wise; and interleaving theplurality of bit groups the order of which is rearranged.

The rearranging in bit group wise may include rearranging the order ofthe plurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method isQPSK, and the code rate is 5/15, π(j) in Equation 21 may be defined asin Table 32.

The interleaving the plurality of bit groups may include interleaving bywriting the plurality of bit groups in each of a plurality of columns inbit group wise in a column direction, and reading each row of theplurality of columns in which the plurality of bit groups are written inbit group wise in a row direction.

The interleaving the plurality of bit groups may include seriallywriting, in the plurality of columns, at least some bit groups which arewritable in the plurality of columns in bit group wise from among theplurality of bit groups, and then dividing and writing the other bitgroups in an area which remains after the at least some bit groups arewritten in the plurality of columns in bit group wise.

According to various exemplary embodiments, improved decoding andreceiving performance can be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describing indetail exemplary embodiments, with reference to the accompanyingdrawings, in which:

FIG. 1 is a block diagram to illustrate a configuration of atransmitting apparatus according to an exemplary embodiment;

FIGS. 2 to 4 illustrate a configuration of a parity check matrixaccording to various exemplary embodiments;

FIG. 5 is a block diagram to illustrate a configuration of aninterleaver according to an exemplary embodiment;

FIGS. 6 to 8 illustrate an interleaving method according to exemplaryembodiments;

FIGS. 9 to 15 illustrate an interleaving method of a block interleaveraccording to exemplary embodiments;

FIG. 16 illustrates an operation of a demultiplexer according to anexemplary embodiment;

FIGS. 17 to 19 illustrate a method for extracting interleavingparameters according to exemplary embodiments;

FIG. 20 is a block diagram to illustrate a configuration of a receivingapparatus according to an exemplary embodiment;

FIG. 21 is a block diagram to illustrate a configuration of adeinterleaver according to an exemplary embodiment;

FIG. 22 illustrates a deinterleaving method of a block deinterleaveraccording to an exemplary embodiment; and

FIG. 23 is a flowchart to illustrate an interleaving method according toan exemplary embodiment.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Hereinafter, various exemplary embodiments will be described in greaterdetail with reference to the accompanying drawings.

In the following description, same reference numerals are used for thesame elements when they are depicted in different drawings. The mattersdefined in the description, such as detailed construction and elements,are provided to assist in a comprehensive understanding of the exemplaryembodiments. Thus, it is apparent that the exemplary embodiments can becarried out without those specifically defined matters. Also, functionsor elements known in the related art are not described in detail sincethey would obscure the exemplary embodiments with unnecessary detail.

FIG. 1 is a block diagram to illustrate a configuration of atransmitting apparatus according to an exemplary embodiment. Referringto FIG. 1 , the transmitting apparatus 100 includes an encoder 110, aninterleaver 120, and a modulator 130 (or a constellation mapper).

The encoder 110 generates a low density parity check (LDPC) codeword byperforming LDPC encoding based on a parity check matrix. To achievethis, the encoder 110 may include an LDPC encoder (not shown) to performthe LDPC encoding.

Specifically, the encoder 110 LDPC-encodes information word (orinformation) bits to generate the LDPC codeword which is formed of theinformation word bits and parity bits (that is, LDPC parity bits). Here,bits input to the encoder 110 may be used to the information word bits.Also, since an LDPC code is a systematic code, the information word bitsmay be included in the LDPC codeword as they are.

The LDPC codeword is formed of the information word bits and the paritybits. For example, the LDPC codeword is formed of N_(ldpc) number ofbits, and includes K_(ldpc) umber of information word bits andN_(parity)=N_(ldpc)−K_(ldpc) number of parity bits.

In this case, the encoder 110 may generate the LDPC codeword byperforming the LDPC encoding based on the parity check matrix. That is,since the LDPC encoding is a process for generating an LDPC codeword tosatisfy H·C^(T)=0, the encoder 110 may use the parity check matrix whenperforming the LDPC encoding. Herein, H is a parity check matrix and Cis an LDPC codeword.

For the LDPC encoding, the transmitting apparatus 100 may include amemory and may pre-store parity check matrices of various formats.

For example, the transmitting apparatus 100 may pre-store parity checkmatrices which are defined in Digital Video Broadcasting-Cable version 2(DVB-C2), Digital Video Broadcasting-Satellite-Second Generation(DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial(DVB-T2), etc., or may pre-store parity check matrices which are definedin the North America digital broadcasting standard system AdvancedTelevision System Committee (ATSC) 3.0 standards, which are currentlybeing established. However, this is merely an example and thetransmitting apparatus 100 may pre-store parity check matrices of otherformats in addition to these parity check matrices.

Hereinafter, a parity check matrix according to various exemplaryembodiments will be explained in detail with reference to the drawings.In the parity check matrix, elements other than elements having 1 have0.

For example, the parity check matrix according to an exemplaryembodiment may have a configuration of FIG. 2 .

Referring to FIG. 2 , a parity check matrix 200 is formed of aninformation word submatrix (or an information submatrix) 210corresponding to information word bits, and a parity submatrix 220corresponding to parity bits.

The information word submatrix 210 includes K_(ldpc) number of columnsand the parity submatrix 220 includes N_(parity)=N_(ldpc)−K_(ldpc)number of columns. The number of rows of the parity check matrix 200 isidentical to the number of columns of the parity submatrix 220,N_(parity)=N_(ldpc)−K_(ldpc).

In addition, in the parity check matrix 200, N_(ldpc) is a length of anLDPC codeword, K_(ldpc) is a length of information word bits, andN_(parity)=N_(ldpc)−K_(ldpc) is a length of parity bits. The length ofthe LDPC codeword, the information word bits, and the parity bits meanthe number of bits included in each of the LDPC codeword, theinformation word bits, and the parity bits.

Hereinafter, the configuration of the information word submatrix 210 andthe parity submatrix 220 will be explained in detail.

The information word submatrix 210 includes K_(ldpc) number of columns(that is, 0^(th) column to (K_(ldpc)−1)^(th) column), and follows thefollowing rules:

First, M number of columns from among K_(ldpc) number of columns of theinformation word submatrix 210 belong to the same group, and K_(ldpc)number of columns is divided into K_(ldpc)/M number of column groups. Ineach column group, a column is cyclic-shifted from an immediatelyprevious column by Q_(ldpc). That is, Q_(ldpc) may be a cyclic shiftparameter value regarding columns in a column group of the informationword submatrix 210 of the parity check matrix 200.

Herein, M is an interval at which a pattern of a column group, whichincludes a plurality of columns, is repeated in the information wordsubmatrix 210 (e.g., M=360), and Q_(ldpc) is a size by which one columnis cyclic-shifted from an immediately previous column in a same columngroup in the information word submatrix 210. Also, M is a common divisorof N_(ldpc) and K_(ldpc) and is determined to satisfyQ_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Here, M and Q_(ldpc) are integers andK_(ldpc)/M is also an integer. M and Q_(ldpc) may have various valuesaccording to a length of the LDPC codeword and a code rate (CR)(or,coding rate).

For example, when M=360 and the length of the LDPC codeword, N_(ldpc),is 64800, Q_(ldpc) may be defined as in Table 1 presented below, and,when M=360 and the length N_(ldpc) of the LDPC codeword is 16200,Q_(ldpc) may be defined as in Table 2 presented below.

TABLE 1 Code Rate N_(ldpc) M Q_(ldpc)  5/15 64800 360 120  6/15 64800360 108  7/15 64800 360  96  8/15 64800 360  84  9/15 64800 360  7210/15 64800 360  60 11/15 64800 360  48 12/15 64800 360  36 13/15 64800360  24

TABLE 2 Code Rate N_(ldpc) M Q_(ldpc)  5/15 16200 360 30  6/15 16200 36027  7/15 16200 360 24  8/15 16200 360 21  9/15 16200 360 18 10/15 16200360 15 11/15 16200 360 12 12/15 16200 360  9 13/15 16200 360  6

Second, when the degree of the 0^(th) column of the i^(th) column group(i=0, 1, . . . , K_(ldpc)/M−1) is D_(i) (herein, the degree is thenumber of value 1 existing in each column and all columns belonging tothe same column group have the same degree), and a position (or anindex) of each row where 1 exists in the 0^(th) column of the i^(th)column group is R_(i,0) ⁽⁰⁾,R_(i,0) ⁽¹⁾, . . . , R_(i,0) ^((D) ^(i) ⁻¹⁾,an index R_(i,j) ^((k)) of a row where k^(th) 1 is located in the j^(th)column in the i^(th) column group is determined by following Equation 1:R _(i,j) ^((k)) =R _(i(j−1)) ^((k)) +Q _(ldpc) mod(N _(ldpc) −K_(ldpc))  (1),where k=0, 1, 2, . . . D_(i)−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1,2, . . . , M−1.

Equation 1 can be expressed as following Equation 2:R _(i,j) ^((k)) ={R _(i,0) ^((k))+(j mod M)×Q _(ldpc)} mod(N _(ldpc) −K_(ldpc))  (2),where k=0, 1, 2, . . . D_(i)−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1,2, . . . , M−1. Since j=1, 2, . . . , M−1, (j mod M) of Equation 2 maybe regarded as j.

In the above equations, R_(i,j) ^((k)) is an index of a row where k^(th)1 is located in the j^(th) column in the i^(th) column group, N_(ldpc)is a length of an LDPC codeword, K_(ldpc), is a length of informationword bits, D_(i) is a degree of columns belonging to the i^(th) columngroup, M is the number of columns belonging to a single column group,and Q_(ldpc) is a size by which each column in the column group iscyclic-shifted.

As a result, referring to these equations, when only R_(i,0) ^((k)) isknown, the index R_(i,j) ^((k)) of the row where the k^(th) 1 is locatedin the j^(th) column in the i^(th) column group can be known. Therefore,when the index value of the row where the k^(th) 1 is located in the0^(th) column of each column group is stored, a position of column androw where 1 is located in the parity check matrix 200 having theconfiguration of FIG. 2 (that is, in the information word submatrix 210of the parity check matrix 200) can be known.

According to the above-described rules, all of the columns belonging tothe i^(th) column group have the same degree D_(i). Accordingly, theLDPC codeword which stores information on the parity check matrixaccording to the above-described rules may be briefly expressed asfollows.

For example, when N_(ldpc) is 30, K_(ldpc), is 15, and Q_(ldpc) is 3,position information of the row where 1 is located in the 0^(th) columnof the three column groups may be expressed by a sequence of Equations 3and may be referred to as “weight-1 position sequence”.R _(1,0) ⁽¹⁾=1,R _(1,0) ⁽²⁾=2,R _(1,0) ⁽³⁾=8,R _(1,0) ⁽⁴⁾=10,R _(2,0) ⁽¹⁾=0,R _(2,0) ⁽²⁾=9,R _(2,0) ⁽³⁾=13,R _(3,0) ⁽¹⁾=0,R _(3,0) ⁽²⁾=14.  (3),where R_(i,j) ^((k)) is an index of a row where k^(th) 1 is located inthe j^(th) column in the i^(th) column group.

The weight-1 position sequence like Equation 3 which expresses an indexof a row where 1 is located in the 0^(th) column of each column groupmay be briefly expressed as in Table 3 presented below:

TABLE 3 1 2 8 10 0 9 13 0 14

Table 3 shows positions of elements having value 1 in the parity checkmatrix, and the i^(th) weight-1 position sequence is expressed byindexes of rows where 1 is located in the 0^(th) column belonging to thei^(th) column group.

The information word submatrix 210 of the parity check matrix accordingto an exemplary embodiment may be defined as in Tables 4 to 21 presentedbelow, based on the above descriptions.

Specifically, Tables 4 to 21 show indexes of rows where 1 is located inthe 0^(th) column of the i^(th) column group of the information wordsubmatrix 210. That is, the information word submatrix 210 is formed ofa plurality of column groups each including M number of columns, andpositions of 1 in the 0^(th) column of each of the plurality of columngroups may be defined by Tables 4 to 21.

Herein, the indexes of the rows where 1 is located in the 0^(th) columnof the i^(th) column group mean “addresses of parity bit accumulators”.The “addresses of parity bit accumulators” have the same meaning asdefined in the DVB-C2/S2/T2 standards or the ATSC 3.0 standards whichare currently being established, and thus, a detailed explanationthereof is omitted.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, thecode rate is 5/15, and M is 360, the indexes of the rows where 1 islocated in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are as shown in Table 4 presented below:

TABLE 4 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 245 449 491 980 1064 1194 1277 1671 2026 3186 4399 49005283 5413 5558 6570 7492 7768 7837 7984 8306 8483 8685 9357 9642 1004510179 10261 10338 10412  1 1318 1584 1682 1860 1954 2000 2062 3387 34413879 3931 4240 4302 4446 4603 5117 5588 5675 5793 5955 6097 6221 64496616 7218 7394 9535 9896 10009 10763  2 105 472 735 911 1168 1450 25502851 3277 3624 4128 4460 4572 4669 4783 5102 5133 5199 5905 6647 70287086 7703 8121 8217 9149 9304 9476 9736 9884  3 1217 5338 5737 8334  4855 994 2979 9443  5 7506 7811 9212 9982  6 848 3313 3380 3990  7 20954113 4620 9946  8 1488 2396 6130 7483  9 1002 2241 7067 10418 10 20083199 7215 7502 11 1161 7705 8194 8534 12 2316 4803 8649 9359 13 125 18803177 14 1141 8033 9072

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 5 or 6presented below:

TABLE 5 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 432 655 893 942 1285 1427 1738 2199 2441 2565 2932 32014144 4419 4678 4963 5423 5922 6433 6564 6656 7478 7514 7892  1 220 453690 826 1116 1425 1488 1901 3119 3182 3568 3800 3953 4071 4782 5038 55556836 6871 7131 7509 7850 8317 8443  2 300 454 497 930 1757 2145 23142372 2467 2819 3191 3256 3699 3984 4538 4965 5461 5742 5912 6135 66497636 8078 8455  3 24 65 565 609 990 1319 1394 1465 1918 1976 2463 29873330 3677 4195 4240 4947 5372 6453 6950 7065 8412 8500 8599  4 1373 46685324 7777  5 189 3930 5766 6877  6 3 2961 4207 5747  7 1108 4768 67437106  8 1282 2274 2750 6204  9 2279 2587 2737 6344 10 2889 3164 72758040 11 133 2734 5081 8386 12 437 3203 7121 13 4280 7128 8490 14 6194563 6206 15 2799 6814 6991 16 244 4212 5925 17 1719 7657 8554 18 531895 6685 19 584 5420 6856 20 2958 5834 8103

TABLE 6 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 553 742 9011327 1544 2179 2519 3131 3280 3603 378937924253 5340 5934 5962 6004 6698 7793 8001 8058 8126 8276 8559  1 503590 598 1185 1266 1336 1806 2473 3021 3356 3490 3680 3936 4501 4659 58916132 6340 6602 7447 8007 8045 80598249  2 795 831 9471330 1502 2041 23282513 2814 2829 4048 4802 6044 6109 6461 6777 6800 7099 7126 8095 84288519 8556 8610  3 601 787 8991757 2259 2518 2783 2816 2823 2949 339643304494 4684 4700 4837 4881 4975 5130 5464 65546912 7094 8297  4 42295628 7917 7982  5 1506 3374 4174 5547  6 4275 5650 8208 8533  7 15041747 3433 6345  8 3659 6955 7575 7852  9 607 3002 4913 6453 10 3533 68607895 8048 11 4094 6366 8314 12 2208 4513 5411 13 32 3882 5149 14 3893121 4626 15 1308 4419 6520 16 2092 2373 6849 17 1815 3679 7152 18 35823979 6948 19 1049 2135 3754 20 2276 4442 6591

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 7 or 8presented below:

TABLE 7 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 350 462 1291 1383 1821 2235 2493 3328 3353 3772 38723923 4259 4426 4542 4972 5347 6217 6246 6332 6386  1 177 869 1214 12531398 1482 1737 2014 2161 2331 3108 3297 3438 4388 4430 4456 4522 47835273 6037 6395  2 347 501 658 966 1622 1659 1934 2117 2527 3168 32313379 3427 3739 4218 4497 4894 5000 5167 5728 5975  3 319 398 599 11431796 3198 3521 3886 4139 4453 4556 4635 4688 4753 4986 5199 5224 54965698 5724 6123  4 162 257 304 524 945 1695 1855 2527 2780 2902 2958 34393484 4224 4769 4928 5156 5303 5971 6358 6477  5 807 1695 2941 4276  62652 2857 4660 6358  7 329 2100 2412 3632  8 1151 1231 3872 4869  9 15613565 5138 5303 10 407 794 1455 11 3438 5683 5749 12 1504 1985 3563 13440 5021 6321 14 194 3645 5923 15 1217 1462 6422 16 1212 4715 5973 174098 5100 5642 18 5512 5857 6226 19 2583 5506 5933 20 784 1801 4890 214734 4779 4875 22 938 5081 5377 23 127 4125 4704 24 1244 2178 3352 253659 6350 6465 26 1686 3464 4336

TABLE 8 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 212 255 540 967 1033 1517 1538 3124 3408 3800 4373 48644905 5163 5177 6186  1 275 660 1351 2211 2876 3063 3433 4088 4273 45444618 4632 5548 6101 6111 6136  2 279 335 494865 1662 1681 3414 3775 42524595 5272 5471 5796 5907 5986 6008  3 345 352 3094 3188 4297 4338 44904865 5303 6477  4 222 681 1218 3169 3850 4878 4954 5666 6001 6237  5 172512 1536 1559 21792227 3334 4049 6464  6 716 934 1694 2890 3276 36084332 4468 5945  7 1133 1593 1825 2571 3017 4251 5221 5639 5845  8 10761222 6465  9 159 5064 6078 10 374 4073 5357 11 2833 5526 5845 12 15943639 5419 13 1028 1392 4239 14 115 622 2175 15 300 1748 6245 16 27243276 5349 17 1433 6117 6448 18 485 663 4955 19 711 1132 4315 20 177 32664339 21 1171 4841 4982 22 33 1584 3692 23 2820 3485 4249 24 1716 24283125 25 250 2275 6338 26 108 1719 4961

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 11/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 9 or 10presented below:

TABLE 9 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 108 297 703 742 1345 1443 1495 1628 1812 2341 2559 26692810 2877 3442 3690 3755 3904 4264  1 180 211 477 788 824 1090 1272 15781685 1948 2050 2195 2233 2546 2757 2946 3147 3299 3544  2 627 741 11351157 1226 1333 1378 1427 1454 1696 1757 1772 2099 2208 2592 3354 35804066 4242  3 9 795 959 989 1006 1032 1135 1209 1382 1484 1703 1855 19852043 2629 2845 3136 3450 3742  4 230 413 801 829 1108 1170 1291 17591793 1827 1976 2000 2423 2466 2917 3010 3600 3782 4143  5 56 142 236 3811050 1141 1372 1627 1985 2247 2340 3023 3434 3519 3957 4013 4142 41644279  6 298 1211 2548 3643  7 73 1070 1614 1748  8 1439 2141 3614  9 2841564 2629 10 607 660 855 11 1195 2037 2753 12 49 1198 2562 13 296 11453540 14 1516 2315 2382 15 154 722 4016 16 759 2375 3825 17 162 194 174918 2335 2422 2632 19 6 1172 2583 20 726 1325 1428 21 985 2708 2769 22255 2801 3181 23 2979 3720 4090 24 208 1428 4094 25 199 3743 3757 261229 2059 4282 27 458 1100 1387 28 1199 2481 3284 29 1161 1467 4060 30959 3014 4144 31 2666 3960 4125 32 2809 3834 4318

TABLE 10 Index of row where 1 is located in the 0th column of the ith icolumn group  0 49 719 784 794 968 2382 2685 2873 2974 2995 3540 4179  1272 281 374 1279 2034 2067 2112 3429 3613 3815 3838 4216  2 206 714 8201800 1925 2147 2168 2769 2806 3253 3415 4311  3 62 159 166 605 1496 17112652 3016 3347 3517 3654 4113  4 363 733 1118 2062 2613 2736 3143 34273664 4100 4157 4314  5 57 142 436 983 1364 2105 2113 3074 3639 3835 41644242  6 870 921 950 1212 1861 2128 2707 2993 3730 3968 3983 4227  7 1852684 3263  8 2035 2123 2913  9 883 2221 3521 10 1344 1773 4132 11 4383178 3650 12 543 756 1639 13 1057 2337 2898 14 171 3298 3929 15 16262950 3503 16 484 3050 3323 17 2283 2336 4189 18 2732 4132 4318 19 2252335 3497 20 600 2245 2658 21 1240 2790 3020 22 301 1097 3539 23 12221267 2594 24 1364 2004 3603 25 1142 1185 2147 26 564 1505 2086 27 697991 2908 28 1467 2073 3462 29 2574 2818 3637 30 748 2577 2772 31 11511419 4129 32 164 1238 3401

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 13/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 11 or 12presented below:

TABLE 11 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 37 144 161 199 2213 495 510 589 731 808 834 955 12491264 1311 1377 1460 1520 1595 1707 1955 2055 2099 2154  1 20 27 165 462546 583 742 796 1095 1110 1129 1145 1169 1190 1254 1363 1383 1463 17181835 1870 1879 2108 2128  2 280 362 463 505 638 691 745 861 1006 10831124 1175 1247 1275 1337 1353 1378 1506 1588 1632 1720 1868 1980 2135  3405 464 478 511 566 574 641 766 785 802 836 996 1128 1239 1247 1449 14911537 1616 1643 1668 1950 1975 2149  4 86 192 245 357 363 374 700 713 852903 992 1174 1245 1277 1342 1369 1381 1417 1463 1712 1900 1962 2053 2118 5 101 327 378 550  6 186 723 1318 1550  7 118 277 504 1835  8 199 4071776 1965  9 387 1253 1328 1975 10 62 144 1163 2017 11 100 475 572 213612 431 865 1568 2055 13 283 640 981 1172 14 220 1038 1903 2147 15 4831318 1358 2118 16 92 961 1700 1810 17 132 403 1485 2042 18 431 1110 11301365 19 587 1005 1205 1588 20 704 1113 1943 21 375 1487 2100 22 15071950 2210 23 962 1613 2038 24 554 1295 1501 25 488 784 1446 26 871 19351964 27 54 1475 1504 28 1579 1617 2074 29 1856 1967 2131 30 330 15822107 31 40 1056 1809 32 1310 1353 1410 33 232 554 1939 34 168 641 109935 333 437 1556 36 153 622 745 37 719 931 1188 35 237 638 1607

TABLE 12 Index of row where 1 is located in the 0th column of the ith icolumn group  0 71 334 645 779 786 1124 1331 1267 1379 1554 1766 17981939  1 6 183 364 503 512 922 972 981 1039 1121 1537 1840 2111  2 6 71153 204 253 268 781 799 873 1118 1194 1661 2036  3 6 247 353 581 921 9401108 1146 1208 1268 1511 1527 1671  4 6 37 466 548 747 1142 1203 12731512 1516 1837 1904 2125  5 6 171 863 953 1025 1244 1378 1396 1723 17831816 1914 2121  6 1268 1360 1647 1769  7 6 458 1231 1414  8 183 535 12441277  9 107 360 498 1456 10 6 2007 2059 2120 11 1480 1523 1670 1927 12139 573 711 1790 13 6 1541 1889 2023 14 6 374 957 1174 15 287 423 8721285 16 6 1809 1918 17 65 818 1396 18 590 766 2107 19 192 814 1843 20775 1163 1256 21 42 735 1415 22 334 1008 2055 23 109 596 1785 24 406 5341852 25 684 719 1543 26 401 465 1040 27 112 392 621 28 82 897 1950 29887 1962 2125 30 793 1088 2159 31 723 919 1133 32 610 839 1302 33 2181080 1816 34 627 1646 1749 35 496 1165 1741 36 916 1055 1662 37 182 722945 38 5 595 1674

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 13 presentedbelow:

TABLE 13 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 1606 3402 4961 6751 7132 11516 12300 12482 12592 1334213764 14123 21576 23946 24533 25376 25667 26836 31799 34173 36462 3615336740 37085 37152 37468 37658  1 4621 5007 6910 8732 9757 11508 1309915513 16335 18052 19512 21319 23663 25628 27208 31333 32219 33003 3323933447 36200 36473 33938 37201 37283 37495 38642  2 16 1054 2020 30804194 5098 5631 6877 7689 8237 9804 10067 11017 11366 13136 13354 1537918934 20199 24522 26172 28666 30386 32714 36390 37015 37162  3 700 8971708 6017 6490 7372 7825 9646 10398 16605 18561 18745 21625 22137 2369324340 24066 25015 26995 28586 28895 29687 33938 34520 34858 37056 38297 4 159 2010 2373 3617 4452 4958 5556 5832 6481 8227 9924 10836 1495415594 16623 18065 19249 22394 22677 23408 23731 24076 24776 27007 2822230343 38371  5 3118 3545 4768 4992 5227 6732 8170 9397 10522 11508 1553620218 21921 28599 29445 29758 29968 31014 32027 33685 34378 35867 3632336728 36870 38335 38623  6 1264 4254 6936 9165 9486 9950 10861 1165313697 13961 15164 15665 18444 19470 20313 21189 24371 26431 26999 2808628251 29261 31981 34015 35850 36129 37186  7 111 1307 1628 2041 25245358 7988 8191 10322 11905 12919 14127 15515 15711 17061 19024 2119522902 23727 24401 24608 25111 25228 27338 35398 37794 38196  8 961 30357174 7948 13355 13607 14971 18189 18339 18665 18875 19142 20615 2113621309 21758 23366 24745 25849 25982 27583 30006 31118 32106 36469 3658337920  9 2990 3549 4273 4808 5707 6021 6509 7456 8240 10044 12262 1266013085 14750 15680 16049 21587 23997 25803 28343 28693 34393 34860 3549036021 37737 38296 10 955 4323 5145 6885 8123 9730 11840 12216 1919420313 23056 24248 24830 25268 26617 26801 28557 29753 30745 31450 3197332839 33025 33296 35710 37366 37509 11 264 605 4181 4483 5156 7238 886310939 11251 12964 16254 17511 20017 22395 22818 23261 23422 24064 2632927723 28186 30434 31956 33971 34372 36764 38123 12 520 2562 2794 35283860 4402 5676 6963 8655 9018 9783 11933 16336 17193 17320 19035 2060623579 23769 24123 24966 27866 32457 34011 34499 36620 37526 13 1010610637 10906 34242 14 1856 15100 19378 21848 15 943 11191 27806 29411 164575 6359 13629 19383 17 4476 4953 18782 24313 18 5441 6381 21840 3594319 9638 9763 12546 30120 20 9587 10626 11047 25700 21 4088 15298 2876835047 22 2332 6363 8782 28863 23 4625 4933 28298 30289 24 3541 491818257 31746 25 1221 25233 26757 34892 26 8150 16677 27934 30021 27 850025016 33043 38070 28 7374 10207 16189 35811 29 611 18480 20064 38261 3025416 27352 36089 38469 31 1667 17614 25839 32776 32 4118 12481 2191237945 33 5573 13222 23619 31271 34 18271 26251 27182 30587 35 1469026430 26799 34355 36 13688 16040 20716 34558 37 2740 14957 23436 3254038 3491 14365 14681 36858 39 4796 6238 25203 27854 40 1731 12816 1734426025 41 19182 21662 23742 27872 42 6502 13641 17509 34713 43 1224612372 16746 27452 44 1589 21528 30621 34003 45 12328 20515 30651 3143246 3415 22656 23427 36395 47 632 5209 25958 31085 48 619 3690 1964837778 49 9528 13581 26965 36447 50 2147 26249 26968 28776 51 15698 1820930683 52 1132 19888 34111 53 4608 25513 38874 54 475 1729 34100 55 734832277 38587 56 182 16473 33082 57 3865 9678 21265 58 4447 20151 27618 596335 14371 38711 60 704 9695 28858 61 4856 9757 30546 62 1993 1936130732 63 756 28000 29138 64 3821 24076 31813 65 4611 12326 32291 66 762821515 34995 67 1246 13294 30068 68 6466 33233 35865 69 14484 23274 3815070 21269 36411 37450 71 23129 26195 37653

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 7/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 14 presentedbelow:

TABLE 14 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 7 15 26 69 1439 3712 5756 5792 5911 8456 10579 1946219782 21709 23214 25142 26040 30206 30475 31211 31427 32105 32989 3308233502 34116 34241 34288 34292 34318 34373 34390 34465  1 83 1159 22716500 6807 7823 10344 10700 13367 14162 14242 14352 15015 17301 1895220811 24974 25795 27868 28081 33077 33204 33262 33350 33516 33677 3368033930 34090 34250 34290 34277 34398  2 25 2281 2995 3321 6006 7482 842811489 11601 14011 17409 26210 29945 30675 31101 31355 31451 31543 3169732056 32216 33282 33453 33487 33696 34044 34107 34213 34247 34261 3427634467 34495  3 0 43 87 2530 4485 4595 9951 11212 12270 12344 15566 2133524699 26580 28518 28564 28812 29821 30418 31467 31871 32513 32597 3318733402 33706 33828 33932 33977 34084 34283 34440 34473  4 81 3344 55407711 13308 15400 15885 18265 18632 22209 23654 27736 29158 29701 2984530409 30654 38055 31420 31604 32519 32901 33267 33444 33525 33712 3387834031 34172 34432 34496 34502 34541  5 42 50 66 2501 4706 6715 6970 86379999 14555 22776 26479 27442 27984 28534 39587 31309 31783 31907 3192731934 32313 32369 32830 33364 33434 33553 33654 33725 33889 33962 3446734482  6 6534 7122 8723 13137 13183 15818 18307 19324 20017 26389 2932631464 32678 33668 34217  7 50 113 2119 5038 5581 6397 6550 10987 2230825141 25943 29299 30186 33240 33399  8 7262 8787 9246 10032 10505 1309014587 14790 16374 19946 21129 25726 31033 33660 33675  9 5004 5087 52917949 9477 11845 12698 14585 15239 17486 18100 18259 21409 21789 24280 1028 82 3939 5007 6682 10312 12485 14384 21570 25512 26612 26854 3037131114 32689 11 437 3055 9100 9517 12369 19030 19950 21328 24196 2423625928 28458 30013 32181 33560 12 18 3590 4832 7053 8919 21149 2425626543 27266 30747 31839 32671 33089 33571 34296 13 2678 4569 4667 65517639 10057 24276 24563 25818 26592 27879 28028 29444 29873 34017 14 7277 2874 9092 10041 13669 20676 20778 25566 28470 28888 30338 31772 3214333939 15 296 2196 7309 11901 14025 15733 16768 23587 25489 30936 3153333749 34331 34431 34507 16 6 8144 12490 13275 14140 18706 20251 2064421441 21938 23703 34190 34444 34463 34495 17 5108 14499 15734 1922224695 25667 28359 28432 30411 30720 34161 34386 34465 34511 34522 18 6189 3042 5524 12128 22505 22700 22919 24454 30526 33437 34114 34188 3449034502 19 11 83 4668 4856 6361 11633 15342 16393 16958 26613 29136 3091732559 34346 34504 20 3185 9728 25062 21 1643 5531 21573 22 2285 608824083 23 78 14678 19119 24 49 13705 33535 25 21192 32280 32781 26 1075321469 22084 27 10082 11950 13889 28 7861 25107 29167 29 14051 3417134430 30 706 894 8316 31 29693 30445 32281 32 10202 30964 34448 33 1581532453 34463 34 4102 21608 24740 35 4472 29399 31435 36 1162 7118 2322637 4791 33548 34096 38 1084 34099 34418 39 1765 20745 33714 40 130221300 33655 41 33 8736 16646 42 53 18671 19089 43 21 572 2028 44 333911506 16745 45 285 6111 12643 46 27 10336 11586 47 21046 32728 34538 4822215 24195 34026 49 19975 26938 29374 50 16473 26777 34212 51 20 2926032784 52 35 31645 32837 53 26132 34410 34495 54 12446 20649 26851 556796 10992 31061 56 0 46 8420 57 10 636 22885 58 7183 16342 18305 59 15604 28258 60 6071 18675 34489 61 16786 25023 33323 62 3573 5081 1092563 5067 31761 34415 64 3735 33534 34522 65 85 32829 34518 66 6555 2336834559 67 22083 29335 29390 68 6738 21110 34316 69 120 4192 11123 70 33134144 20824 71 27783 28550 31034 72 6597 8164 34427 73 18009 23474 3246074 94 6342 12656 75 17 31962 34535 76 15091 24955 28545 77 15 3213 2829878 26562 30236 34537 79 16832 20334 24628 80 4841 20669 26509 81 1805523700 34534 82 23576 31496 34492 83 10699 13826 34440

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 8/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 15 presentedbelow:

TABLE 15 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 2768 3039 4059 5856 6245 7013 8157 9341 9802 10470 1152112083 16610 18361 20321 24601 27420 28206 29788  1 2730 8244 8891 915712624 12973 15534 16622 16919 18402 18780 19854 20220 20543 22306 2554627478 27678 28053  2 1727 2268 6246 7815 9010 9556 10134 10472 1138914509 15719 16294 17342 17666 18850 22058 25579 25860 29207  3 28 13463721 5565 7019 9240 12355 13109 14800 16040 16839 17369 17631 1935719473 19891 20381 23911 29683  4 869 2450 4386 5316 6160 7107 1036211132 11271 13149 16397 16532 17113 19894 22043 22784 27383 28615 28804 5 508 4292 5831 8559 10044 10412 11288 14810 15888 17243 17538 1990320528 22090 22652 27235 27384 28208 28485  6 389 2248 5840 6043 70009054 11075 11760 12217 12565 13587 15403 19422 19528 21493 25142 2777728566 28702  7 1015 2002 5764 6777 9346 9629 11039 11153 12690 1306813990 16841 17702 20021 24106 26300 29332 30081 30196  8 1480 3084 34674401 4798 5187 7851 11368 12323 14325 14546 16360 17158 18010 2133325612 26556 26906 27005  9 6925 8876 12392 14529 15253 15437 19226 1995020321 23021 23651 24393 24653 26668 27205 28269 28529 29041 29292 102547 3404 3538 4666 5126 5468 7695 8799 14732 15072 15881 17410 1897119609 19717 22150 24941 27908 29018 11 888 1581 2311 5511 7218 910710454 12252 13662 15714 15894 17025 18671 23404 25316 25556 25489 2897729212 12 1047 1494 1718 4645 5030 6811 7868 8146 10611 15767 17682 1839122614 23021 23763 25478 26491 29088 29757 13 59 1781 1900 3814 4121 80448906 9175 11156 14841 15789 16033 16755 17292 18550 19310 22505 2956429850 14 1952 3057 4399 9476 10171 10769 11335 11569 15002 19501 2062122642 23452 24360 25109 25290 25828 28505 29122 15 2895 3070 3437 47644965 6670 8244 11845 13352 13573 13975 14600 15871 17996 19672 2097920579 25327 27958 16 612 1528 2004 4244 4599 4926 5843 7684 10122 1044312267 14368 18413 19058 22985 24257 26202 26596 27899 17 1361 2195 41466708 7158 7588 9138 9998 14862 15359 16076 18925 21401 21573 22503 2414624247 27778 29312 18 5229 6235 7134 7655 9139 13527 15408 16058 1670518320 19909 20901 22238 22437 23654 25131 27550 28247 29903 19 697 20354887 8275 6909 9166 11805 15338 16381 18403 20425 20688 21547 2459025171 16726 28848 29224 29412 20 5379 17329 22659 23062 21 11814 1475922329 22936 22 2423 2811 10296 12727 23 8460 15260 16769 17290 24 1419114608 29536 30187 25 7103 10069 20111 22850 26 4285 15413 26448 29069 27548 2137 9189 10925 28 4581 7077 23382 23940 29 3942 17248 19486 2792230 8668 10230 16922 26678 31 6158 9980 13788 28198 32 12422 16076 2420629887 33 8778 10649 18747 22111 34 21029 22677 27150 28980 35 7918 1542327672 27803 36 5927 18086 23525 37 3397 15058 30224 38 24016 25880 2626839 1096 4775 7912 40 3259 17301 20802 41 129 8396 15132 42 17825 2811928676 43 2343 8382 28840 44 3907 18374 20939 45 1132 1290 8786 46 14814710 28846 47 2185 3705 26834 48 5496 15681 21854 49 12697 13407 2217850 12788 21227 22894 51 629 2854 6232 52 2289 18227 27458 53 7593 2193523001 54 3836 7081 12282 55 7925 18440 23135 56 497 6342 9737 57 1119922046 30067 58 12572 28045 28990 59 1240 2023 10933 60 19566 20629 2518661 6442 13303 28813 62 4765 10572 16180 63 552 19301 24286 64 6782 1848021383 65 11267 12288 15758 66 771 5652 15531 67 16131 20047 25649 6813227 23035 24450 69 4839 13467 27488 70 2852 4677 22993 71 2504 2811629524 72 12518 17374 24267 73 1222 11859 27922 74 966017285 18261 75 23211296 29978 76 9750 11165 16295 77 4894 9505 23622 78 10861 11980 1411079 2128 15883 22836 80 6274 17243 21989 81 10866 13202 22517 82 1115916111 21608 83 3719 18787 22100 84 1756 2920 23901 85 20913 29473 3010386 2729 16091 26976 87 4410 8217 12963 88 5395 24564 28235 89 3859 1790923051 90 5733 26005 29797 91 1935 3492 29773 92 11903 21380 29914 936091 10469 29997 94 2895 8930 15594 95 1827 10028 20070

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 9/15, and M is 360, the indexes of the rowswhere 1 is located in the 0^(th) column of the i^(th) column group ofthe information word submatrix 210 are as shown in Table 16 presentedbelow:

TABLE 16 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 113 1557 3316 5680 6241 10707 13404 13947 14040 1435315522 15698 16079 17363 19374 19543 20530 22833 24339  1 271 1361 62367006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 2393825351 25590 25876 25910  2 73 605 872 4008 6279 7653 10346 10799 1248212935 13604 15909 16526 19782 20506 22804 23629 24856 25600  3 1445 16904304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 2195822451 23869 23999 24177  4 1290 2337 5661 6371 8996 10102 10941 1136012242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913  5 2842 1926 3421 3503 8558 9453 10168 15820 17473 10571 19685 22790 2333623367 23890 24061 25657 25680  6 0 1709 4041 4932 5968 7123 8430 956410596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863  7 291625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 2194124137 24269 24416 24803 25154 25395  8 55 66 871 3700 11426 13221 1500116367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872 9 1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 2526225566 25668 25679 25858 25888 25915  10 7520 7690 8855 9183 14654 1669517121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 2529325403  11 48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 2303323107 23128 23990 24286 24409 24595 25802  12 12 51 3894 4539 8276 1088511644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 2546325838  13 3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 2131022547 22756 22959 24768 24814 25594 25626 25880  14 21 29 69 1448 23864601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 2443125512 25814  15 18 53 7890 9934 10063 16728 19040 19809 20825 2152221800 23582 24556 25031 25547 25562 25733 25789 25906  16 4096 4582 57665894 6517 10027 12182 13247 15207 17041 18958 20133 20503 22228 2438224613 25689 25855 25883  17 0 25 819 5539 7076 7536 7605 9532 1366815051 17683 19665 20253 21996 24136 24890 25758 25784 25807  18 34 40 444215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 2441824873 25107 25644  19 1595 6216 22850 25439  20 1562 15172 19517 22362 21 7508 12879 24324 24496  22 6298 15819 16757 18721  23 11173 1517519966 21195  24 59 13505 16941 23793  25 2267 4830 12023 20587  26 88279278 13072 16664  27 14419 17463 23398 25348  28 6112 16534 20423 22698 29 493 8914 21103 24799  30 6896 12761 13206 25873  31 2 1380 1232221701  32 11600 21306 25753 25790  33 8421 13076 14271 15401  34 963014112 19017 20955  35 212 13932 21781 25824  36 5961 9119 16654 19636 37 58 5434 9936 12770  38 6575 11433 19798  39 2731 7338 20926  4014253 18463 25404  41 21791 24805 25869  42 2 11646 15850  43 6075 858623819  44 18435 22083 24852  45 2103 2368 11704  46 10925 17402 18232 47 9062 25061 25674  48 18497 20853 23404  49 18606 19364 19551  50 71022 25543  51 6744 15481 25868  52 9081 17305 25164  53 8 23701 25883 54 9680 19955 22845  55 56 4564 19121  56 5595 15086 25892  57 317417127 23186  58 19397 19817 20275  59 12561 24571 25825  60 7111 988925865  61 19104 20189 21851  62 549 9686 25548  63 6586 20325 25905  643224 20710 21537  65 641 15215 25754  66 13484 23729 25818  67 2043 749324246  68 16860 25230 25768  69 22047 24200 24902  70 9391 18040 19499 71 7855 24336 25069  72 23834 25570 25852  73 1977 8800 25756  74 667121772 25859  75 3279 6710 24444  76 24099 25117 25820  77 5553 1230625915  78 48 11107 23907  79 10832 11974 25773  80 2223 17905 25484  8116782 18135 20446  82 475 2861 3457  83 16218 22449 24362  84 1171622200 25897  85 8315 15009 22633  86 13 20480 25852  87 12352 1865825687  88 3681 14794 23703  89 30 24531 25846  90 4103 22077 24107  9123837 25622 25812  92 3627 13387 25839  93 908 5367 19388  94 0 689425795  95 20322 23546 25181  96 8178 25260 25437  97 2449 13244 22565 98 31 18928 22741  99 1312 5134 14838 100 6085 13937 24220 101 66 1463325670 102 47 22512 25472 103 8867 24704 25279 104 6742 21623 22745 105147 9948 24178 106 8522 24261 24307 107 19202 22406 24609

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 10/15, and M is 360, the indexes of rows where 1is located in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 17 or 18below:

TABLE 17 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 979 1423 4166 4609 6341 8258 10334 10548 14098 1451417051 17333 17653 17830 17990  1 2559 4025 6344 6510 9167 9728 1131214856 17104 17721 18600 18791 19079 19697 19840  2 3243 6894 7950 1053912042 13233 13938 14752 16449 16727 17025 18297 18796 19400 21577  33272 3574 6341 6722 9191 10807 10957 12531 14036 15580 16651 17007 1730919415 19845  4 155 4598 10201 10975 11086 11296 12713 15364 15978 1639517542 18164 18451 18612 20617  5 1128 1999 3926 4069 5558 6085 6337 838610693 12450 15438 16223 16370 17308 18634  6 2408 2929 3630 4357 58527329 8536 8695 10603 11003 14304 14937 15767 18402 21502  7 199 30666446 3849 8973 9536 10452 12857 13675 15913 16717 17654 19802 2011521579  8 312 870 2095 2586 5517 6208 i.757 7311 7368 1304615384 1857620349 21424 21587  9 985 1591 3248 3509 3706 3847 6174 6276 7864 903313618 15675 16446 18355 18843  10 975 3774 4083 5825 6166 7218 7633 965710103 13052 14240 17320 18126 19544 20208  11 1795 2005 2544 3418 61488051 9066 9725 10676 10752 11512 15171 17523 20481 21059  12 167 3151824 2325 2640 2868 6070 6597 7016 8109 9815 11608 16142 17912 19625  131298 1896 3039 4303 4690 8787 12241 13600 14478 15492 16602 17115 1791319466 20597  14 568 3695 6045 6524 8131 8404 8590 9059 9246 11570 1433618657 18941 19218 21506  15 228 1889 1967 2299 3011 5074 7044 7596 76899534 10244 10697 11691 17902 21410  16 1330 1579 1739 2234 3701 38655713 6677 7263 11172 12143 12765 17121 20011 21436  17 303 1668 25014925 5778 5985 9635 10140 10820 11779 11849 12058 15650 20426 20527  18698 2484 3071 3219 4054 4125 5663 5939 6928 7086 8054 12173 16280 1794519302  19 232 1619 3040 4901 7438 8135 9117 9233 10131 13321 17347 1743618193 18586 19929  20 12 3721 6254 6609 7880 8139 10437 12262 1392814065 14149 15032 15694 16264 18883  21 482 915 1548 1637 6687 933810163 11768 11970 15524 15695 17386 18787 19210 19340  22 1291 2500 41094511 5099 5194 10014 13165 13256 13972 15409 16113 16214 18584 20998  231761 4778 7444 7740 8129 8341 8931 9136 9207 10003 10678 13959 1767318194 20990  24 3060 3522 5361 5692 6833 8342 8792 11023 11211 1154811914 13987 15442 15541 19707  25 1322 2348 2970 5632 6349 7577 87829113 9267 9376 12042 12943 16680 16970 21321  26 6785 11960 21455  271223 15672 19550  28 5976 11335 20385  29 2818 9387 15317  30 2763 355418102  31 5230 11489 18997  32 5809 15779 20674  33 2620 17838 18533  343025 9342 9931  35 3728 5337 12142  36 2520 6666 9164  37 12892 1530720912  38 10736 12393 16539  39 1075 2407 12853  40 4921 5411 18206  415955 15647 16838  42 6384 10336 19266  43 429 10421 17266  44 4880 1043112208  45 2910 11895 12442  46 7366 18362 18772  47 4341 7903 14994  484564 6714 7378  49 4639 8652 18871  50 15787 18048 20246  51 3241 1107913640  52 1559 2936 15881  53 2737 6349 10881  54 10394 16107 17073  558207 9043 12874  56 7805 16058 17905  57 11189 15767 17764  58 582312923 14316  59 11080 20390 20924  60 568 8263 17411  61 1845 3557 6562 62 2890 10936 14756  63 9031 14220 21517  64 3529 12955 15902  65 4136750 8735  66 6784 12092 16421  67 12019 13794 15308  68 12588 1537817676  69 8067 14589 19304  70 1244 5877 6085  71 15897 19349 19993  721426 2394 12264  73 3456 8931 12075  74 13342 15273 20351  75 9138 1335220798  76 7031 7626 14081  77 4280 4507 15617  78 4170 10569 14335  793839 7514 16578  80 4688 12815 18782  81 4861 7858 9435  82 605 544512912  83 2280 4734 7311  84 6668 8128 12638  85 3733 10621 19534  8613933 18316 19341  87 1786 3037 21566  88 2202 13239 16432  89 4882 58089300  90 4580 8484 16754  91 14630 17502 18269  92 6889 11119 12447  938162 9078 16330  94 6538 17851 18100  95 17763 19793 20816  96 218311907 17567  97 6640 14428 15175  98 877 12035 14081  99 1336 6468 12328100 5948 9146 12003 101 3782 5699 12445 102 1770 7946 8244 103 738412639 14989 104 1469 11586 20959 105 7943 10450 15907 106 5005 815310035 107 17750 18826 21513 108 4725 8041 10112 109 3837 16266 17376 11011340 17361 17512 111 1269 4611 4774 112 2322 10813 16157 113 1675216843 18959 114 70 4325 18753 115 3165 8153 15384 116 160 8045 16823 11714112 16724 16792 118 4291 7667 18176 119 5943 19879 20721

TABLE 18 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 316 1271 3672 9495 12147 12849 14928 16671 16938 1786419108 20502 21097 21115  1 2341 2559 2643 2816 2865 5137 5331 7000 75238023 10439 10797 13208 15041  2 5556 6858 7677 10162 10207 11349 1232112398 14787 15743 15859 15952 19313 20879  3 349 573 910 2702 3654 62149246 9353 10638 11772 14447 14953 16620 19888  4 204 1390 2887 3835 62306533 7443 7876 0209 10201 10836 11360 18287 20086  5 541 2429 2535 71445523 8537 10490 :10,85 11074 12074 113752 19812 17900 18548  6 733 16953538 5323 5503 7882 9429 10582 13997 19909 18844 14.387 10592 20904  71134 2136 4631 4633 4718 1197 10410 11555 14995 13305 19048 17417 18119020303  8 714 1001 1283 4959 10016 19176 10973 31578 12051 15559 1591519022 10410 20121  9 745 4057 5855 9885 10594 10989 13156 13219 1335113631 13685 14577 17713 20386  10 968 1446 2130 2502 3092 3787 5323 81048418 9998 11681 13972 17747 17929  11 3020 3857 5275 5786 6319 860811943 14062 17144 17752 18001 18453 19311 21414  12 709 747 1038 21815320 8292 10584 10859 13964 15009 15277 16953 20675 21509  13 1663 32475003 5760 7186 7360 10346 14211 14717 14792 15155 16128 17355 17970  14516 578 1914 6147 9419 11148 11434 13289 13325 13332 19106 19257 2096221556  15 5009 5632 6531 9430 9886 10621 11765 13969 16178 16413 1811018249 20616 20759  16 457 2686 3318 4608 5620 5858 6480 7430 9602 1269114664 18777 20152 20848  17 33 2877 5334 6851 7907 8654 10688 1540116123 17942 17969 18747 18931 20224  18 87 897 7636 8663 11425 1228812672 14199 16435 17615 17950 18953 19667 20281  19 1042 1832 2545 27192947 3672 3700 6249 6398 6833 11114 14283 17694 20477  20 326 488 26622880 3009 5357 6587 8882 11604 14374 18781 19051 19057 20508  21 8541294 2436 2852 4903 6466 7761 9072 9564 10321 13638 15658 16946 19119 22 194 899 1711 2408 2786 5391 7108 8079 8716 11453 17303 19484 2098921389  23 1631 3121 3994 5005 7810 8850 10315 10589 13407 17162 1862418758 19311 20301  24 736 2424 4792 5600 6370 10061 16053 15775 18600 25 1254 8163 8876 9157 12141 14587 16545 17175 18191  26 388 6641 897410607 10716 14477 15825 17191 18400  27 5578 6082 6824 7360 7745 865511402 11665 12428  28 3603 8729 13463 14698 15210 19112 19550 2072721052  29 48 1732 3805 5158 15442 16909 19854 21071 21579  30 1170714014 21531  31 1542 4133 4925  32 10083 13505 21198  33 14300 1576516752  34 778 1237 11215  35 1325 3199 14534  36 2007 14510 20599  371996 5881 16429  38 5111 15018 15980  39 4989 10681 12810  40 3763 1071516515  41 2259 10080 15642  42 9032 11319 21305  43 3915 15213 20884  4411150 15022 20201  45 1147 6749 19625  46 12139 12939 18870  47 38404634 10244  48 1018 10231 17720  49 2708 13056 13393  50 5781 1158818888  51 1345 2036 5252  52 5908 8143 15141  53 1804 13693 18640  5410433 13965 16950  55 9568 10122 15945  56 547 6722 14015  57 321 1284414095  58 2632 10513 14936  59 6369 11995 20321  60 9920 19136 21529  611990 2726 10183  62 5763 12118 15467  63 503 10006 19564  64 9839 1194219472  65 11205 13552 15389  66 8841 13797 19697  67 124 6053 18224  686477 14406 21146  69 1224 8027 16011  70 3046 4422 17717  71 739 1230817760  72 4014 4130 7835  73 2266 5652 11981  74 2711 7970 18317  752196 15229 17217  76 8636 13302 16764  77 5612 15010 16657  78 615 12494639  79 3821 12073 18506  80 1066 16522 21536  81 11307 18363 19740  823240 8560 10391  83 3124 11424 20779  84 1604 8861 17394  85 2083 74008093  86 3218 7454 9155  87 9855 15998 20533  88 316 2850 20652  89 55839768 10333  90 7147 7713 18339  91 12607 17428 21418  92 14216 1695418164  93 8477 15970 18488  94 1632 8032 9751  95 4573 9080 13507  9611747 12441 13876  97 1183 15605 16675  98 4408 10264 17109  99 54957882 12150 100 1010 3763 5065 101 9828 18054 21599 102 6342 7353 15358103 6362 9462 19999 104 7184 13693 17622 105 4343 4654 10995 106 70998466 18520 107 11505 14395 15138 108 6779 16691 18726 109 7146 1264420196 110 5865 16728 19634 111 4657 8714 21246 112 4580 5279 18750 1133767 6620 18905 114 9209 13093 17575 115 12486 15875 19791 116 804614636 17491 117 2120 4643 13206 118 6186 9675 12601 119 784 5770 21585

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 11/15, and M is 360, the indexes of rows where 1is located in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 19 below.

TABLE 19 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 696 989 1238 3091 3116 3738 4269 6406 7033 8048 915710254 12033 16456 16912  1 444 1488 6541 8626 10735 12447 13111 1370614135 15195 15947 16453 16916 17137 17268  2 401 460 992 1145 1576 16782238 2320 4280 6770 1027 12486 15363 16714 17157  3 1161 3108 3727 45085092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205  4 5421190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 1704017063  5 17 487 776 880 5077 6172 9771 11446 12798 16016 16109 1617117087 17132 17226  6 1337 3275 3462 4229 9246 10180 10845 10866 1225013633 14482 16024 16812 17186 17241  7 15 980 2305 3674 5971 822 41149911752 11770 12897 14082 14836 15311 16391 17209  8 0 3926 5869 8696 93519391 11371 14052 14172 14636 14974 16619 16961 17033 17237  9 3033 53176501 65/9 10698 12158 12966 14019 15392 15806 1599.1 16493 16690 1706217090  10 981 1205 4400 6410 11003 13319 13405 14695 15846 16297 1649216563 16616 16862 16953  11 1725 4276 8869 9588 14062 14486 15474 1554816300 16432 17042 17050 17060 17175 17273  12 1807 5921 9960 10011 1430514490 14872 15852 16054 16061 16306 16799 16833 17136 17262  13 28264752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 1717917247  14 1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 1601116421 16825 17112 17195  15 2890 4821 5987 7226 8823 9869 12468 1469415352 15805 16075 16462 17102 17251 17263  16 3751 3890 4382 5720 1028110411 11350 12721 13121 14127 14980 15202 15335 16735 17123  17 26 302805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103 18 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 1627417034 17225 17266  19 904 3157 6284 7151 7984 11712 12887 13767 1554716099 16753 16829 17044 17250 17259  20 7 311 4876 8334 9249 11267 1407214559 15003 15235 15686 16331 17177 17238 17253  21 4410 8066 8596 963110369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204  22 248261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 1708417193 17220  23 88 11622 14735 15890  24 304 2026 2638 6018  25 11634268 11620 17232  26 9701 11785 14463 17260  27 4118 10952 12224 17006 28 3647 10823 11521 12060  29 1717 3753 9199 11642  30 2187 14280 17220 31 14787 16903 17061  32 381 3534 4294  33 3149 6947 8323  34 1256216724 16881  35 7289 9997 15306  36 5615 13152 17260  37 5666 1692617027  38 4190 7798 16831  39 4778 10629 17180  40 10001 13884 15453  416 2237 8203  42 7831 15144 15160  43 9186 17204 17243  44 9435 1716817237  45 42 5701 17159  46 7812 14259 15715  47 39 4513 6658  48 389368 11273  49 1119 4785 17182  50 5620 16521 16729  51 16 6685 17242 52 210 3452 12383  53 466 14462 16250  54 10548 12633 13962  55 14526005 16453  56 22 4120 13684  57 5195 11563 16522  58 5518 16705 17201 59 12233 14552 15471  60 6067 13440 17248  61 8660 8967 17061  62 867312176 15051  63 5959 15767 16541  64 3244 12109 12414  65 16936 1712217162  66 4868 8451 13183  67 3714 4451 16919  68 11313 13801 17132  6917070 17191 17242  70 1911 11201 17186  71 14 17190 17254  72 1176016008 16832  73 14543 17033 17278  74 16129 16765 17155  75 6891 1556117007  76 12741 14744 17116  77 8992 16661 17277  78 1861 11130 16742 79 4822 13331 16192  80 13281 14027 14989  81 38 14887 17141  82 1069813452 15674  83 4 2539 16877  84 857 17170 17249  85 11449 11906 12867 86 285 14118 16831  87 15191 17214 17242  88 39 728 16915  89 246912969 15579  90 16644 17151 17164  91 2592 8280 10448  92 9236 1243117173  93 9064 16892 17233  94 4526 16146 17038  95 31 2116 16083  9615837 16951 17031  97 5362 8382 16618  98 6137 13199 17221  99 284115068 17068 100 24 3620 17003 101 9880 15718 16764 102 1784 10240 17209103 2731 10293 10846 104 3121 8723 16598 105 8563 15662 17088 106 131167 14676 107 29 13850 15963 108 3654 7553 8114 109 23 4362 14865 1104434 14741 16688 111 8362 13901 17244 112 13687 16736 17232 113 46 422913394 114 13169 16383 16972 115 16031 16681 16952 116 3384 9894 12580117 9841 14414 16165 118 5013 17099 17115 119 2130 8941 17266 120 690715428 17241 121 16 1860 17235 122 2151 16014 16643 123 14954 15958 17222124 3969 8419 15116 125 31 15593 16984 126 11514 16605 17255

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 12/15, and M is 360, the indexes of rows where 1is located in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 20 below.

TABLE 20 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 584 1472 1621 1867 3338 3568 3723 4185 5126 5889 77378632 8940 9725  1 221 445 590 3779 3835 6939 7743 8280 8448 8491 936710042 11242 12917  2 4662 4837 4900 5029 6449 6687 6751 8684 9936 1168111811 11886 12089 12909  3 2418 3018 3647 4210 4473 7447 7502 9490 1006711092 11139 11256 12201 12383  4 2591 2947 3349 3406 4417 4519 5176 66728498 8863 9201 11294 11376 12184  5 27 101 197 290 871 1727 3911 54116676 8703 9350 10310 10798 12489  6 1765 1897 2923 3584 3901 4048 69637054 7032 9165 10184 10824 11278 12669  7 2183 3740 4808 5217 5660 63756787 8219 8466 9037 10353 10583 11118 12762  8 73 1594 2146 2715 35013572 3639 3725 6959 7187 8406 10120 10507 10691  9 240 732 1215 23892788 2830 3499 3881 4197 4991 6425 7061 9756 10491  10 831 1568 18283424 4319 4516 4639 6018 9702 10203 10417 11240 11518 12458  11 20242970 3048 3638 3676 4152 5284 5779 5926 9426 9945 10873 11787 11837  121049 1218 1651 2328 3493 4363 5750 6483 7613 8782 9738 9803 11744 11937 13 1193 2060 2289 2964 3478 4592 4756 6709 7162 8231 8326 11140 1190812243  14 978 2120 2439 3338 3850 4589 6567 8745 9656 9708 10161 1054210711 12639  15 2403 2938 3117 3247 3711 5593 5844 5932 7801 10152 1022611498 12162 12941  16 1781 2229 2276 2533 3582 3951 5279 5774 7930 982410920 11038 12340 12440  17 289 384 1980 2230 3464 3873 5958 8656 89429006 10175 11425 11745 12530  18 155 354 1090 1330 2002 2236 3559 37054922 5958 6576 8564 9972 12760  19 303 876 2059 2142 5244 5330 6644 75768614 9598 10410 10718 11033 12957  20 3449 3617 4408 4602 4727 6182 88358928 9372 9644 10237 10747 11655 12747  21 811 2565 2820 8677 8974 963211069 11548 11839 12107 12411 12695 12812 12890  22 972 4123 4943 63856449 7339 7477 8379 9177 9359 10074 11709 12552 12831  23 842 973 15412262 2905 5276 6758 7099 7894 8128 8325 8663 8875 10050  24 474 791 9683902 4924 4965 5085 5908 6109 6329 7931 9038 9401 10568  25 1397 44614658 5911 6037 7127 7318 8678 8924 9000 9473 9602 10446 12692  26 13347571 12881  27 1393 1447 7972  28 633 1257 10597  29 4843 5102 11056  303294 8015 10513  31 1108 10374 10546  32 5353 7824 10111  33 3398 76748569  34 7719 9478 10503  35 2997 9418 9581  36 5777 6519 11229  37 19665214 9899  38 6 4088 5827  39 836 9248 9612  40 483 7229 7548  41 78658289 9804  42 2915 11098 11900  43 6180 7096 9481  44 1431 6786 8924  45748 6757 8625  46 3312 4475 7204  47 1852 8958 11020  48 1915 2903 4006 49 6776 10886 12531  50 2594 9998 12742  51 159 2002 12079  52 853 32813762  53 5201 5798 6413  54 3882 6062 12047  55 4133 6775 9657  56 2286874 11183  57 7433 10728 10864  58 7735 8073 12734  59 2844 4621 11779 60 3909 7103 12804  61 6002 9704 11060  62 5864 6856 7681  63 3652 58697605  64 2546 2657 4461  65 2423 4203 9111  66 244 1855 4691  67 11062178 6371  68 391 1617 10126  69 250 9259 10603  70 3435 4614 6924  711742 8045 9529  72 7667 8875 11451  73 4023 6108 6911  74 8621 1018411650  75 6726 10861 12348  76 3228 6302 7388  77 1 1137 5358  78 3812424 8537  79 3256 7508 10044  80 1980 2219 4569  81 2468 5699 10319  822803 3314 12808  83 8578 9642 11533  84 829 4585 7923  85 59 329 5575 86 1067 5709 6867  87 1175 4744 12219  88 109 2518 6756  89 2105 1062611153  90 5192 10696 10749  91 6260 76418233  92 2998 3094 11214  933398 6466 11494  94 6574 10448 12160  95 2734 10755 12780  96 1028 795810825  97 8545 8602 10793  98 392 3398 11417  99 6639 9291 12571 1001067 7919 8934 101 1064 2848 12753 102 6076 8656 12690 103 5504 619310171 104 1951 7156 7356 105 4389 4780 7889 106 526 4804 9141 107 12383648 10464 108 2587 5624 12557 109 5560 5903 11963 110 1134 2570 3297111 10041 11583 12157 112 1263 9585 12912 113 3744 7898 10646 114 459074 10315 115 1051 6188 10038 116 2242 8394 12712 117 3598 9025 12651118 2295 3540 5610 119 1914 4378 12423 120 1766 3635 12759 121 5177 958611143 122 943 3590 11649 123 4864 6905 10454 124 5852 6042 10421 1256095 8285 12349 126 2070 7171 8563 127 718 12234 12716 128 512 1066711353 129 3629 6485 7040 130 2880 8865 11466 131 4490 10220 11796 1325440 8819 9103 133 5262 7543 12411 134 516 7779 10940 135 2515 5843 9202136 4684 5994 10586 137 573 2270 3324 138 7870 8317 10322 139 6856 763812909 140 1583 7669 10781 141 8141 9085 12555 142 3903 5485 9992 1434467 11998 12904

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 13/15, and M is 360, the indexes of rows where 1exists in the 0^(th) column of the i^(th) column group of theinformation word submatrix 210 are defined as shown in Table 21 below:

TABLE 21 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 142 2307 2598 2650 4028 4434 5781 5881 6016 6323 66816698 8125  1 2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 85398583  2 899 3295 3433 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602 3 3080 4120 5429 5636 5937 6966 8110 8170 8247 8355 8365 8616  4 201745 2838 3799 4380 4418 4646 5059 7343 8164 8302 8456 8631  5 9 62746725 6797 7393 7333 8027 8186 8209 8273 8442 8348 8632  6 494 1365 24053799 5188 5291 7644 7926 8139 8458 8504 8594 8625  7 192 574 1179 43874695 5089 5831 7673 7789 8298 9301 8612 8632  8 11 20 1406 6111 61766256 6708 6834 7828 8232 8457 8495 8602  9 6 2654 3554 4483 4966 58666795 8069 8249 8301 8497 8509 8623  10 21 1144 2355 3124 6773 6805 68877742 7994 8358 8374 8580 8611  11 335 4473 4883 5528 6096 7543 7586 79218197 8319 8394 8489 8636  12 2919 4331 4419 4735 6366 6393 6844 71938165 8205 8544 8586 8617  13 12 19 742 930 3009 4330 6213 6224 7292 74307792 7922 8137  14 710 1439 1588 2434 3516 5239 6248 6827 8230 8448 85158581 8619  15 200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 83918526  16 3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636 17 3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598  18105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587  19 7871857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537  20 15 11184226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568  21 36 5216 53685616 6029 6591 8038 8067 8299 8351 8565 8578 8585  22 1 23 4300 45305426 5532 5817 6967 7124 7979 8022 8270 8437  23 629 2133 4828 5475 58755890 7194 8042 8345 8385 8518 8598 8612  24 11 1065 3782 4237 4993 71047863 7904 8104 8228 8321 8383 8565  25 2131 2274 3168 3215 3220 55976347 7812 8238 8354 8527 8557 8614  26 5600 6591 7491 7696  27 1766 82818626  28 1725 2280 5120  29 1650 3445 7652  30 4312 6911 8626  31 151013 5892  32 2263 2546 2979  33 1545 5873 7406  34 67 726 3697  35 28606443 8542  36 17 911 2820  37 1561 4580 6052  38 79 5269 7134  39 222410 2424  40 3501 5642 8627  41 808 6950 8571  42 4099 6389 7482  434023 5000 7833  44 5476 5765 7917  45 1008 3194 7207  46 20 495 5411  471703 8388 8635  48 6 4395 4921  49 200 2053 8206  50 1089 5126 5562  5110 4193 7720  52 1967 2151 4608  53 22 738 3513  54 3385 5066 8152  55440 1118 8537  56 3429 6058 7716  57 5213 7519 8382  58 5564 8365 8620 59 43 3219 8603  60 4 5409 5815  61 5 6376 7654  62 4091 5724 5953  635348 6754 8613  64 1634 6398 6632  65 72 2058 8605  66 3497 5811 7579 67 3846 6743 8559  68 15 5933 8629  69 2133 5859 7068  70 4151 46178566  71 2960 8270 8410  72 2059 3617 8210  73 544 1441 6895  74 40437482 8592  75 294 2180 8524  76 3058 8227 8373  77 364 5756 8617  785383 8555 8619  79 1704 2480 4181  80 7338 7929 7990  81 2615 3905 7981 82 4298 4548 8296  83 8262 8319 8630  84 892 1893 8028  85 5694 72378595  86 1487 5012 5810  87 4335 8593 8624  88 3509 4531 5273  89 10 22830  90 4161 5208 6280  91 275 7063 8634  92 4 2725 3113  93 2279 74038174  94 1637 3328 3930  95 2810 4939 5624  96 3 1234 7687  97 2799 77408616  98 22 7701 8636  99 4302 7857 7993 100 7477 7794 8592 101 9 61118591 102 5 8606 8628 103 347 3497 4033 104 1747 2613 8636 105 1827 56007042 106 580 1822 6842 107 232 7134 7783 108 4629 5000 7231 109 951 28064947 110 571 3474 8577 111 2437 2496 7945 112 23 5873 8162 113 12 11687686 114 8315 8540 8596 115 1766 2506 4733 116 929 1516 3338 117 21 12166555 118 782 1452 8617 119 8 6083 6087 120 667 3240 4583 121 4030 46615790 122 559 7122 8553 123 3202 4388 4909 124 2533 3673 8594 125 19913954 6206 126 6835 7900 7980 127 189 5722 8573 128 2680 4928 4998 129243 2579 7735 130 4281 8132 8566 131 7656 7671 8609 132 1116 2291 4166133 21 388 8021 134 6 1123 8369 135 311 4918 8511 136 0 3248 6290 137 136762 7172 138 4209 5632 7563 139 49 127 8074 140 581 1735 4075 141 02235 5470 142 2178 5820 6179 143 16 3575 6054 144 1095 4564 6458 145 91581 5953 146 2537 6469 8552 147 14 3874 4844 148 0 3269 3551 149 21147372 7926 150 1875 2388 4057 151 3232 4042 6663 152 9 401 583 153 134100 6584 154 2299 4190 4410 155 21 3670 4979

According to an exemplary embodiment, even when the order of numbers ina sequence corresponding to the i^(th) column group of the parity checkmatrix 200 as shown in the above-described Tables 4 to 21 is changed,the changed parity check matrix is a parity check matrix used for thesame code. Therefore, a case in which the order of numbers in thesequence corresponding to the i^(th) column group in Tables 4 to 21 ischanged is covered by the inventive concept.

According to an exemplary embodiment, even when the arrangement order ofsequences corresponding to each column group is changed in Tables 4 to21, cycle characteristics on a graph of a code and algebraiccharacteristics such as degree distribution are not changed. Therefore,a case in which the arrangement order of the sequences shown in Tables 4to 21 is changed is also covered by the inventive concept.

In addition, even when a multiple of Q_(ldpc) is equally added to allsequences corresponding to a certain column group in Tables 4 to 21, thecycle characteristics on the graph of the code or the algebraiccharacteristics such as degree distribution are not changed. Therefore,a result of equally adding a multiple of Q_(ldpc) to the sequences shownin Tables 4 to 21 is also covered by the inventive concept. However, itshould be noted that, when the resulting value obtained by adding themultiple of Q_(ldpc) to a given sequence is greater than or equal to(N_(ldpc)−K_(ldpc)), a value obtained by applying a modulo operation for(N_(ldpc)−K_(ldpc)) to the resulting value should be applied instead.

Once positions of the rows where 1 exists in the 0^(th) column of thei^(th) column group of the information word submatrix 210 are defined asshown in Tables 4 to 21, positions of rows where 1 exists in anothercolumn of each column group may be defined since the positions of therows where 1 exists in the 0^(th) column are cyclic-shifted by Q_(ldpc)in the next column.

For example, in the case of Table 4, in the 0^(th) column of the 0^(th)column group of the information word submatrix 210, 1 exists in the245^(th) row, 449^(th) row, 491^(st) row, . . . .

In this case, since Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M=(16200-5400)/360=30,the indexes of the rows where 1 is located in the 1^(st) column of the0^(th) column group may be 275(=245+30), 479(=449+30), 521(=491+30), . .. , and the indexes of the rows where 1 is located in the 2^(nd) columnof the 0^(th) column group may be 305(=275+30), 509(=479+30),551(=521+30), . . . .

In the above-described method, the indexes of the rows where 1 islocated in all rows of each column group may be defined.

The parity submatrix 220 of the parity check matrix 200 shown in FIG. 2may be defined as follows:

The parity submatrix 220 includes N_(ldpc)−K_(ldpc) number of columns(that is, K_(ldpc) ^(th) column to (N_(ldpc)−1)^(th) column), and has adual diagonal or staircase configuration. Accordingly, the degree ofcolumns except the last column (that is, (N_(ldpc)−1)^(th) column) fromamong the columns included in the parity submatrix 220 is 2, and thedegree of the last column is 1.

As a result, the information word submatrix 210 of the parity checkmatrix 200 may be defined by Tables 4 to 21, and the parity submatrix220 of the parity check matrix 200 may have a dual diagonalconfiguration.

When the columns and rows of the parity check matrix 200 shown in FIG. 2are permutated based on Equation 4 and Equation 5, the parity checkmatrix shown in FIG. 2 may be changed to a parity check matrix 300 shownin FIG. 3 .Q _(ldpc) ·i+j⇒M·j+i(0≤i<M,0≤j<Q _(ldpc))  (4)K _(ldpc) +Q _(ldpc) ·k+l⇒K _(ldpc) +M·l+k(0≤k≤M,0≤l<Q _(ldpc))  (5)

The method for permutating based on Equation 4 and Equation 5 will beexplained below. Since row permutation and column permutation apply thesame principle, the row permutation will be explained by the way of anexample.

In the case of the row permutation, regarding the X^(th) row, i and jsatisfying X=Q_(ldpc)×i+j are calculated and the X^(th) row ispermutated by assigning the calculated i and j to M×j+i. For example,regarding the 7^(th) row, i and j satisfying 7=2×i+j are 3 and 1,respectively. Therefore, the 7^(th) row is permutated to the 13^(th) row(10×1+3=13).

When the row permutation and the column permutation are performed in theabove-described method, the parity check matrix of FIG. 2 may beconverted into the parity check matrix of FIG. 3 .

Referring to FIG. 3 , the parity check matrix 300 is divided into aplurality of partial blocks, and a quasi-cyclic matrix of M×Mcorresponds to each partial block.

Accordingly, the parity check matrix 300 having the configuration ofFIG. 3 is formed of matrix units of M×M. That is, the submatrices of M×Mare arranged in the plurality of partial blocks, constituting the paritycheck matrix 300.

Since the parity check matrix 300 is formed of the quasi-cyclic matricesof M×M, M number of columns may be referred to as a column block and Mnumber of rows may be referred to as a row block. Accordingly, theparity check matrix 300 having the configuration of FIG. 3 is formed ofN_(qc_column)=N_(ldpc)/M number of column blocks andN_(qc_row)=N_(parity)/M number of row blocks.

Hereinafter, the submatrix of M×M will be explained.

First, the (N_(qc_column)−1)^(th) column block of the 0^(th) row blockhas a form shown in Equation 6 presented below:

$\begin{matrix}{{A =}\begin{bmatrix}0 & 0 & \ldots & 0 & 0 \\1 & 0 & \ldots & 0 & 0 \\0 & 1 & \ldots & 0 & 0 \\\vdots & \vdots & \vdots & \vdots & \vdots \\0 & 0 & \ldots & 1 & 0\end{bmatrix}} & (6)\end{matrix}$

As described above, A 330 is an M×M matrix, values of the 0^(th) row andthe (M−1)^(th) column are all “0”, and, regarding 0≤i≤(M−2), the(i+1)^(th) row of the i^(th) column is “1” and the other values are “0”.

Second, regarding 0≤i≤(N_(ldpc)−K_(ldpc))/M−1 in the parity submatrix320, the i^(th) row block of the (K_(ldpc)/M+i)^(th) column block isconfigured by a unit matrix I_(M×M) 340. In addition, regarding0≤i≤(N_(ldpc)−K_(ldpc))/M−2, the (i+1)^(th) row block of the(K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M)340.

Third, a block 350 constituting the information word submatrix 310 mayhave a cyclic-shifted format of a cyclic matrix P, P^(a) ^(ij) , or anadded format of the cyclic-shifted matrix P^(a) ^(ij) of the cyclicmatrix P (or an overlapping format).

For example, a format in which the cyclic matrix P is cyclic-shifted tothe right by 1 may be expressed by Equation 7 presented below:

$\begin{matrix}{P = \begin{bmatrix}0 & 1 & 0 & \; & 0 \\0 & 0 & 1 & \ldots & 0 \\\vdots & \vdots & \vdots & \; & \vdots \\0 & 0 & 0 & \ldots & 1 \\1 & 0 & 0 & \; & 0\end{bmatrix}} & (7)\end{matrix}$

The cyclic matrix P is a square matrix having an M×M size and is amatrix in which a weight of each of M number of rows is 1 and a weightof each of M number of columns is 1. When a_(ij) is 0, the cyclic matrixP, that is, P⁰ indicates a unit matrix I_(M×M), and when a_(ij) is ∞,P^(∞) is a zero matrix.

A submatrix existing where the i^(th) row block and the j^(th) columnblock intersect in the parity check matrix 300 of FIG. 3 may be P^(a)^(ij) . Accordingly, i and j indicate the number of row blocks and thenumber of column blocks in the partial blocks corresponding to theinformation word. Accordingly, in the parity check matrix 300, the totalnumber of columns is N_(ldpc)=M×N_(qc_column), and the total number ofrows is N_(parity)=M×N_(qc_row). That is, the parity check matrix 300 isformed of N_(qc_column) number of “column blocks” and N_(qc_row) numberof “row blocks”.

Hereinafter, a method for performing LDPC encoding based on the paritycheck matrix 200 as shown in FIG. 2 will be explained. An LDPC encodingprocess when the parity check matrix 200 is defined as shown in Table 10by way of an example will be explained for the convenience ofexplanation.

First, when information word bits having a length of K_(ldpc) are [i₀,i₁, i₂, . . . , i_(K) _(ldp) ⁻¹], and parity bits having a length ofN_(ldpc)−K_(ldpc) are [p₀, p₁, p₂, . . . p_(N) _(ldpc) _(K) _(ldpc) ⁻¹],the LDPC encoding is performed by the following process.

Step 1) Parity bits are initialized as ‘0’. That is, p₀=p₁=p₂= . . .=P_(N) _(ldpc) _(−K) _(ldpc) ⁻¹=0.

Step 2) The 0^(th) information word bit i₀ is accumulated in a paritybit having the address of the parity bit defined in the first row (thatis, the row of i=0) of Table 10 as the index of the parity bit. This maybe expressed by Equation 8 presented below:

$\quad\begin{matrix}\begin{matrix}{P_{49} = {P_{49} \oplus {+ i_{0}}}} & {P_{2685} = {P_{2685} \oplus {+ i_{0}}}} \\{P_{719} = {P_{719} \oplus i_{0}}} & {P_{2873} = {P_{2873} \oplus i_{0}}} \\{P_{784} = {P_{784} \oplus i_{0}}} & {P_{2974} = {P_{2974} \oplus {+ i_{0}}}} \\{P_{794} = {P_{794} \oplus i_{0}}} & {P_{2995} = {P_{2995} \oplus i_{0}}} \\{P_{968} = {P_{968} \oplus i_{0}}} & {P_{3540} = {P_{3540} \oplus {+ i_{0}}}} \\{P_{2382} = {P_{2382} \oplus i_{0}}} & {P_{4179} = {P_{4179} \oplus i_{0}}}\end{matrix} & (8)\end{matrix}$

Herein, i₀ is a 0^(th) information word bit, p_(i) is an ith parity bit,and ⊕ is a binary operation. According to the binary operation, 1⊕1equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 3) The other 359 information word bits i_(m) (m=1, 2, . . . , 359)are accumulated in the parity bit. The other information word bits maybelong to the same column group as that of i₀. In this case, the addressof the parity bit may be determined based on Equation 9 presented below:(x+(m mod 360)×Q _(ldpc))mod(N _(ldpc) −K _(ldpc))  (9)

Herein, x is an address of a parity bit accumulator corresponding to theinformation word bit i₀, and Q_(ldpc) is a size by which each column iscyclic-shifted in the information word submatrix, and may be 12 in thecase of Table 10. In addition, since m=1, 2, . . . , 359, (m mod 360) inEquation 9 may be regarded as m.

As a result, information word bits i_(m) (m=1, 2, . . . , 359) areaccumulated in the parity bits having the address of the parity bitcalculated based on Equation 9 as the index. For example, an operationas shown in Equation 10 presented below may be performed for theinformation word bit i₁:

$\quad\begin{matrix}\begin{matrix}{P_{61} = {P_{61} \oplus i_{1}}} & {P_{2697} = {P_{2697} \oplus i_{1}}} \\{P_{731} = {P_{731} \oplus i_{1}}} & {P_{2885} = {P_{2885} \oplus i_{1}}} \\{P_{796} = {P_{796} \oplus i_{1}}} & {P_{2986} = {P_{2986} \oplus i_{1}}} \\{P_{806} = {P_{806} \oplus i_{1}}} & {P_{3007} = {P_{3007} \oplus i_{1}}} \\{P_{980} = {P_{980} \oplus i_{1}}} & {P_{3552} = {P_{3552} \oplus 1_{1}}} \\{P_{2394} = {P_{2394} \oplus i_{1}}} & {P_{4191} = {P_{4191} \oplus i_{1}}}\end{matrix} & (10)\end{matrix}$

Herein, i₁ is a 1^(st) information word bit, p_(i) is an ith parity bit,and ⊕ is a binary operation. According to the binary operation, 1⊕1equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 4) The 360^(th) information word bits i₃₆₀ is accumulated in aparity bit having the address of the parity bit defined in the 2^(nd)row (that is, the row of i=1) of Table 10 as the index of the paritybit.

Step 5) The other 359 information word bits belonging to the same groupas that of the information word bit i₃₆₀ are accumulated in the paritybit. In this case, the address of the parity bit may be determined basedon Equation 9. However, in this case, x is the address of the parity bitaccumulator corresponding to the information word bit i₃₆₀.

Step 6) Steps 4 and 5 described above are repeated for all of the columngroups of Table 10.

Step 7) As a result, a parity bit p_(i) is calculated based on Equation11 presented below. In this case, i is initialized as 1.p _(i) =p _(i) ⊕p _(i−1) i=1,2, . . . ,N _(ldpc) −K _(ldpc)−1  (11)

In Equation 11, p_(i) is an ith parity bit, N_(ldpc), is a length of anLDPC codeword, K_(ldpc) is a length of an information word of the LDPCcodeword, and ⊕ is a binary operation.

As a result, the encoder 110 may calculate the parity bits according tothe above-described method.

In another example, a parity check matrix according to an exemplaryembodiment may have a configuration as shown in FIG. 4 .

Referring to FIG. 4 , the parity check matrix 400 may be formed of 5matrices A, B, C, Z, and D. Hereinafter, the configuration of eachmatrix will be explained to explain the configuration of the paritycheck matrix 400.

First, M₁, M₂, Q₁, and Q₂, which are parameter values related to theparity check matrix 400 as shown in FIG. 4 , may be defined as shown inTable 22 presented below according to the length and the code rate ofthe LDPC codeword.

TABLE 22 Sizes Rate Length M₁ M₂ Q₁ Q₂ 1/15 16200 2520 12600 7  35 648001080 59400 3 165 2/15 16200 3240 10800 9  30 64800 1800 54360 5 151 3/1516200 1080 11880 3  33 64800 1800 50040 5 139 4/15 16200 1080 10800 3 30 64800 1800 45720 5 127 5/15 16200  720 10080 2  28 64800 1440 417604 116 6/15 16200 1080  8640 3  24 64800 1080 37800 3 105

The matrix A is formed of K number of columns and g number of rows, andthe matrix C is formed of K+g number of columns and N−K−g number ofrows. Herein, K is a length of information word bits, and N is a lengthof the LDPC codeword.

Indexes of rows where 1 is located in the 0^(th) column of the ithcolumn group in the matrix A and the matrix C may be defined based onTables 23 to 31 according to the length and the code rate of the LDPCcodeword. In this case, an interval at which a pattern of a column isrepeated in each of the matrix A and the matrix C, that is, the numberof columns belonging to the same group, may be 360.

For example, when the length N of the LDPC codeword is 64800 and thecode rate is 3/15, the indexes of rows where 1 is located in the 0^(th)column of the ith column group in the matrix A and the matrix C aredefined as shown in Table 23 presented below:

TABLE 23 i Index of row where 1 is located in the 0th column of the ithcolumn group  0 920 963 1307 2648 6529 17455 18883 19848 19909 2414924249 38395 41589 48032 50313  1 297 736 744 5951 8438 9881 15522 1645223036 25071 34915 41193 42975 43412 49612  2 10 223 879 4662 6400 869114561 16626 17408 22810 31795 32580 43639 45223 47511  3 629 842 16663150 7596 9465 12327 18649 19052 19279 29743 30197 40106 48371 51155  4857 953 1116 8725 8726 10508 17112 21007 30649 32113 36962 39254 4663649599 50099  5 700 894 1128 5527 6216 15123 21510 24584 29026 3141637158 38460 42511 46932 51832  6 430 592 1521 3018 10430 18090 1809218388 20017 34383 35006 38255 41700 42158 45211  7 91 1485 1733 1162412969 17531 21324 23657 27148 27509 28753 35093 43352 48104 51648  8 1834 117 6739 8679 11018 12163 16733 24113 25906 30605 32700 36465 4079943359  9 481 1545 1644 4216 4606 6015 6609 14659 16966 18056 19137 2667028001 30668 49061 10 174 1208 1387 10580 11507 13751 16344 22735 2355926492 27672 33399 44787 44842 45992 11 1151 1185 1472 6727 10701 1475515688 17441 21281 23692 23994 31366 35854 37301 43148 12 200 799 15833451 5880 7604 8194 13428 16109 18584 20463 22373 31977 47073 50087 13346 843 1352 13409 17376 18233 19119 19382 20578 24183 32052 32912 4320448539 49893 14 76 457 1169 13516 14520 14638 22391 25294 31067 3132536711 44072 44854 49274 51624 15 759 798 1420 6661 12101 12573 1379615510 18384 26649 30875 36856 38994 43634 49281 16 551 797 1000 399910040 11246 15793 23298 23822 38480 39209 45334 46603 46625 47633 17 441875 1554 5336 25948 28842 30329 31503 39203 39673 46250 47021 4855549229 51421 18 963 1470 1642 3180 3943 6513 9125 15641 17083 18876 2849932764 42420 43922 45762 19 293 324 867 8803 10582 17926 19830 2249724848 30034 34659 37721 41523 42534 47806 20 687 975 1356 2721 3002 38744119 12336 17119 21251 22482 22833 24681 26225 48514 21 549 951 12689144 11710 12623 18949 19362 22769 32603 34559 34683 36338 47140 5106922 52 890 1669 3905 5670 14712 18314 22297 30328 33389 35447 35512 3551640587 41918 23 656 1063 1694 3338 3793 4513 6009 7441 13393 20920 2650127576 29623 31261 42093 24 425 1018 1086 9226 10024 17552 24714 2487725853 28918 30945 31205 33103 42564 47214 25 32 1145 1438 4916 494514830 17505 19919 24118 28506 30173 31754 34230 48608 50291 26 559 12161272 2856 8703 9371 9708 16180 19127 24337 26390 36649 41105 42988 4409627 362 658 1191 7769 8998 14068 15921 18471 18780 31995 32798 3286437293 39468 44308 28 1136 1389 1785 8800 12541 14723 15210 15859 2656930127 31357 32898 38760 50523 51715 29 44 80 1368 2010 2228 6614 67679275 25237 30208 39537 42041 49906 50701 51199 30 1522 1536 1765 39145350 10869 12278 12886 16379 22743 23987 26306 30966 33854 41356 31 212648 709 3443 7007 7545 12484 13358 17008 20433 25862 31945 39207 3975240313 32 789 1062 1431 12280 17415 18098 23729 37278 38454 38763 4103944600 50700 51139 51696 33 825 1298 1391 4882 12738 17569 19177 1989627401 37041 39181 39199 41832 43636 45775 34 992 1053 1485 3806 1692918596 22017 23435 23932 30211 30390 34469 37213 46220 49646 35 771 8501039 5180 7653 13547 17980 23365 25318 34374 36115 38753 42993 4969651031 36 7383 14780 15959 18921 22579 28612 32038 36727 40851 4194742707 50480 37 8733 9464 13148 13899 19396 22933 23039 25047 29938 3358833796 48930 38 2493 12555 16706 23905 35400 36330 37065 38866 4030543807 43917 50621 39 6437 11927 14542 16617 17317 17755 18832 2477229273 31136 36925 46663 40 2191 3431 6288 6430 9908 13069 23014 2482229818 39914 46010 47246

In another example, when the length N of the LDPC codeword is 16200 andthe code rate is 4/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 24 presented below:

TABLE 24 Indexes of rows where 1 is located in the 0th column i of theith column group  0 19 585 710 3241 3276 3648 6345 9224 9890 10841  1181 494 894 2562 3201 4382 5130 5308 6493 10135  2 150 569 919 1427 23474475 7857 8904 9903  3 1005 1818 1025 2933 3280 3946 4049 4166 5209  4420 554 778 6908 7959 8344 8462 10912 11099  5 231 506 859 4478 49577664 7731 7908 8980  6 179 537 979 3717 5092 6315 6883 9353 9935  7 147205 830 3609 3720 4667 7441 10196 11809  8 60 1021 1061 1554 4918 56906184 7986 11296  9 145 719 768 2290 2919 7272 8561 9145 10233 10 388 590852 1579 1698 1974 9747 10192 10255 11 231 343 485 1546 3155 4829 771010394 11336 12 4381 5398 5987 9123 10365 11018 11153 13 2381 5196 66136844 7357 8732 11082 14 1730 4599 5693 6318 7626 9231 10663

In another example, when the length N of the LDPC codeword is 64800 andthe code rate is 4/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 25 presented below:

TABLE 25 i Indexes of rows where 1 is located in the 0th column of theith column group  0 276 1754 1780 3597 8549 15196 26305 27003 3388337189 41042 41849 42356  1 730 873 927 9310 9867 17594 21969 25106 2592231167 35434 37742 45866  2 925 1202 1564 2575 2831 2951 5193 13096 1836320592 33786 34090 40900  3 973 1045 1071 8545 8980 11983 18649 2132322789 22843 26821 36720 37856  4 402 1038 1689 2466 2893 13474 1571024137 29709 30451 35568 35966 46436  5 263 271 395 5089 5645 15488 1631428778 29729 34350 34533 39608 45371  6 387 1059 1306 1955 6990 2000124606 28167 33802 35181 38481 38688 45140  7 53 851 1750 3493 1141518882 20244 23411 28715 30722 36487 38019 45416  8 810 1044 1772 39065832 16793 17333 17910 23946 29650 34190 40673 45828  9 97 491 948 1215613788 24970 33774 37539 39750 39820 41195 46464 46820 10 192 899 12833732 7310 13637 13810 19005 24227 26772 31273 37665 44005 11 424 5311300 4860 8983 10137 16323 16888 17933 22458 26917 27835 37931 12 130279 731 3024 6378 18838 19746 21007 22825 23109 28644 32048 34667 13 9381041 1482 9589 10065 11535 17477 25816 27966 35022 35025 42536 14 170454 1312 5326 6765 23408 24090 26072 33037 38088 42985 46413 15 220 804843 2921 4841 7760 8303 11259 21058 21276 34346 37604 16 676 713 83211937 12006 12309 16329 26438 34214 37471 38179 42420 17 714 931 15806837 9824 11257 15556 26730 32053 34461 35889 45821 18 28 1097 1340 87679406 17253 29558 32857 37856 38593 41781 47101 19 158 722 754 1448923851 28160 30371 30579 34963 44216 46462 47463 20 833 1326 1332 70329566 11011 21424 26827 29789 31699 32876 37498 21 251 504 1075 4470 773611242 20397 32719 34453 36571 40344 46341 22 330 581 868 15168 2026526354 33624 35134 38609 44965 45209 46909 23 729 1643 1732 3946 49129615 19699 30993 33658 38712 39424 46799 24 546 982 1274 9264 1101711868 15674 16277 19204 28506 39063 43331 25 73 1160 1196 4334 1256013583 14703 18270 18719 19327 38985 46779 26 1147 1625 1759 3767 591211599 18561 19330 29619 33671 43346 44098 27 104 1507 1586 9387 1789023532 27008 27861 30966 33579 35541 39801 28 1700 1746 1793 4941 781413746 20375 27441 30262 30392 35385 42848 29 183 555 1029 3090 5412 814819662 23312 23933 28179 29962 35514 30 891 908 1127 2827 4077 4376 457026923 27456 33699 43431 46071 31 404 1110 1782 6003 14452 19247 2699830137 31404 31624 46621 47366 32 886 1627 1704 8193 8980 9648 1092816267 19774 35111 38545 44735 33 268 380 1214 4797 5168 9109 9288 1799221309 33210 36210 41429 34 572 1121 1165 6944 7114 20978 23540 2586326190 26365 41521 44690 35 18 185 496 5885 6165 20468 23895 24745 3122633680 37665 38587 36 289 527 1118 11275 12015 18088 22805 24679 2826230160 34892 43212 37 658 926 1589 7634 16231 22193 25320 26057 2651227498 29472 34219 38 337 801 1525 2023 3512 16031 26911 32719 3562039035 43779 44316 39 248 534 670 6217 11430 24090 26509 28712 3307333912 38048 39813 40 82 1556 1575 7879 7892 14714 22404 22773 2553134170 38203 38254 41 247 313 1224 3694 14304 24033 26394 28101 3745537859 38997 41344 42 790 887 1418 2811 3288 9049 9704 13303 14262 3814940109 40477 43 1310 1384 1471 3716 8250 25371 26329 26997 30138 4084241041 44921 44 86 288 367 1860 8713 18211 22628 22811 28342 28463 4041545845 45 719 1438 1741 8258 10797 29270 29404 32096 34433 34616 3603045597 46 215 1182 1364 8146 9949 10498 18603 19304 19803 23685 4330445121 47 1243 1496 1537 8484 8851 16589 17665 20152 24283 28993 3427439795 48 6320 6785 15841 16309 20512 25804 27421 28941 43871 44647 492207 2713 4450 12217 16506 21188 23933 28789 38099 42392 50 14064 1430714599 14866 17540 18881 21065 25823 30341 36963 51 14259 14396 1703726769 29219 29319 31689 33013 35631 37319 52 7798 10495 12868 1429817221 23344 31908 39809 41001 41965

In another example, when the length N of the LDPC codeword is 16200 andthe code rate is 5/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 26 presented below:

TABLE 26 Indexes of rows where 1 is located in the 0th column i of theith column group  0 69 244 706 5145 5994 6066 6763 6815 8509  1 257 541618 3933 6188 7048 7484 8424 9104  2 69 500 536 1494 1669 7075 7553 820210305  3 11 189 340 2103 3199 6775 7471 7918 10530  4 333 400 434 18063264 5693 8534 9274 10344  5 111 129 260 3562 3676 3680 3809 5169 73088280  6 100 303 342 3133 3952 4226 4713 5053 5717 9931  7 83 87 374 8282460 4943 6311 8657 9272 9571  8 114 166 325 2680 4698 7703 7886 87919978 10684  9 281 542 549 1671 3178 3955 7153 7432 9052 10219 10 202 271608 3860 4173 4203 5169 6871 8113 9757 11 16 359 419 3333 4198 4737 61707987 9573 10095 12 235 244 584 4640 5007 5563 6029 6816 7678 9968 13 123449 646 2460 3845 4161 6610 7245 7686 8651 14 136 231 468 835 2622 32925158 5294 6584 9926 15 3085 4683 8191 9027 9922 9928 10550 16 2462 31853976 4091 8089 8772 9342

In another example, when the length N of the LDPC codeword is 64800 andthe code rate is 6/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 27 presented below:

TABLE 27 i Indexes of rows where 1 is located in the 0th column of theith column group  0 221 1011 1218 4299 7143 8728 11072 15533 17356 3390936833  1 360 1210 1375 2313 3493 16822 21373 23588 23656 26267 34098  2544 1347 1433 2457 9186 10945 13583 14858 19195 34606 37441  3 37 596715 4134 8091 12106 24307 24658 34108 40591 42883  4 235 398 1204 20756742 11670 13512 23231 24784 27915 34752  5 204 873 890 13550 1657019774 34012 35249 37655 39885 42890  6 221 371 514 11984 14972 1569028827 29069 30531 31018 43121  7 280 549 1435 1889 3310 10234 1157515243 20748 30469 36005  8 223 666 1248 13304 14433 14732 18943 2124823127 38529 39272  9 370 819 1065 9461 10319 25294 31958 33542 3745839681 40039 10 585 870 1028 5087 5216 12228 16216 16381 16937 2713227893 11 164 167 1210 7386 11151 20413 22713 23134 24188 36771 38992 12298 511 809 4620 7347 8873 19602 24162 29198 34304 41145 13 105 830 12122415 14759 15440 16361 16748 22123 32684 42575 14 659 665 668 6458 2213025972 30697 31074 32048 36078 37129 15 91 808 953 8015 8988 13492 1398715979 28355 34509 39698 16 594 983 1265 3028 4029 9366 11069 11512 2706640939 41639 17 506 740 1321 1484 10747 16376 17384 20285 31502 3892542606 18 338 356 975 2022 3578 18689 18772 19826 22914 24733 27431 19709 1264 1366 4617 8893 25226 27800 29080 30277 37781 39644 20 840 11791338 2973 3541 7043 12712 15005 17149 19910 36795 21 1009 1267 1380 491912679 22889 29638 30987 34637 36232 37284 22 466 913 1247 1646 3049 59249014 20539 34546 35029 36540 23 374 697 984 1654 5870 10883 11684 2029428888 31612 34031 24 117 240 635 5093 8673 11323 12456 14145 21397 3961942559 25 122 1265 1427 13528 14282 15241 16852 17227 34723 36836 3979126 595 1180 1310 6952 17916 24725 24971 27243 29555 32138 35987 27 140470 1017 13222 13253 18462 20806 21117 28673 31598 37235 28 7 710 10728014 10804 13303 14292 16690 26676 36443 41966 29 48 189 759 12438 1452316388 23178 27315 28656 29111 29694 30 285 387 410 4294 4467 5949 2538627898 34880 41169 42614 31 474 545 1320 10506 13186 18126 27110 3149835353 36193 37322 32 1075 1130 1424 11390 13312 14161 16927 25071 2584434287 38151 33 161 396 427 5944 17281 22201 25218 30143 35566 3826142513 34 233 247 694 1446 3180 3507 9069 20764 21940 33422 39358 35 271508 1013 6271 21760 21858 24887 29808 31099 35475 39924 36 8 674 13293135 5110 14460 28108 28388 31043 31137 31863 37 1035 1222 1409 828716083 24450 24888 29356 30329 37834 39684 38 391 1090 1128 1866 409510643 13121 14499 20056 22195 30593 39 55 161 1402 6289 6837 8791 1793721425 26602 30461 37241 40 110 377 1228 6875 13253 17032 19008 2327432285 33452 41630 41 360 638 1355 5933 12593 13533 23377 23881 2458626040 41663 42 535 1240 1333 3354 10860 16032 32573 34908 34957 3925540759 43 526 936 1321 7992 10260 18527 28248 29356 32636 34666 35552 44336 785 875 7530 13062 13075 18925 27963 28703 33688 36502 45 36 5911062 1518 3821 7048 11197 17781 19408 22731 24783 46 214 1145 1223 15469475 11170 16061 21273 38688 40051 42479 47 1136 1226 1423 20227 2257324951 26462 29586 34915 42441 43048 48 26 276 1425 6048 7224 7917 874727559 28515 35002 37649 49 127 294 437 4029 8585 9647 11904 24115 2851436893 39722 50 748 1093 1403 9536 19305 20468 31049 38667 40502 4072041949 51 96 638 743 9806 12101 17751 22732 24937 32007 32594 38504 52649 904 1079 2770 3337 9158 20125 24619 32921 33698 35173 53 401 518 9847372 12438 12582 18704 35874 39420 39503 39790 54 10 451 1077 8078 1632017409 25807 28814 30613 41261 42955 55 405 592 1178 15936 18418 1958521966 24219 30637 34536 37838 56 50 584 851 9720 11919 22544 22545 2585135567 41587 41876 57 911 1113 1176 1806 10058 10809 14220 19044 2074829424 36671 58 441 550 1135 1956 11254 18699 30249 33099 34587 3524339952 59 510 1016 1281 8621 13467 13780 15170 16289 20925 26426 34479 604969 5223 17117 21950 22144 24043 27151 39809 61 11452 13622 18918 1967023995 32647 37200 37399 62 6351 6426 13185 13973 16699 22524 31070 3191663 4098 10617 14854 18004 28580 36158 37500 38552

In another example, when the length N of the LDPC codeword is 16200 andthe code rate is 6/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 28 presented below:

TABLE 28 Indexes of rows where 1 is located in the 0th column i of theith column group  0 15 593 1066 1714 5358 6168 7077 7979  1 339 731 7691399 4678 7100 8114 8696  2 247 344 510 5273 5668 6136 8569 9147  3 21283 521 4055 4548 4957 6557 7718  4 3 110 880 1410 4143 8297 9105 9115 5 2 559 636 1934 2947 3765 4060 5072  6 741 754 1040 1827 2112 33384693 6498  7 213 338 775 2464 2974 3852 4353 4787  8 211 428 432 24392694 4541 6025 8071  9 28 239 855 2060 3791 7217 8722 10 407 555 8142635 3037 4619 8473 11 203 846 988 2599 4890 7749 9671 12 641 682 8012577 4612 4916 5286 13 111 577 728 2998 4109 5547 8002 14 197 391 4801526 9016 9434 9447 15 382 446 546 3865 6824 7752 8076 16 307 321 10314476 7858 8463 9604 17 112 252 446 1665 2189 4869 5570 18 4566 6695 79668371 9608 19 2490 3419 6716 9038 9232 20 1117 1203 6031 7193 7320

In another example, when the length N of the LDPC codeword is 64800 andthe code rate is 6/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 29 presented below:

TABLE 29 Index of row where 1 is located in the 0th column i of the ithcolumn group  0 71 276 856 6867 12964 17373 18159 26420 28460 28477  1257 322 672 2533 5316 6578 9037 10231 13845 36497  2 233 765 904 13663875 13145 15409 18620 23910 30825  3 100 224 405 12776 13866 1478716781 23886 29099 31419  4 23 496 891 2512 12589 14074 19392 20339 2765828684  5 473 712 759 1283 4374 9896 12551 13814 24242 32728  6 511 567815 11823 17106 17900 19338 22315 24396 26448  7 45 733 836 1923 372717468 25746 33806 35995 36657  8 17 487 675 2670 3922 5145 18009 2399331073 36624  9 72 751 773 1937 17324 28512 30666 30934 31016 31849 10257 343 594 14041 19141 24914 26864 28809 32055 34753 11 99 241 491 26509670 17433 17785 18988 22235 30742 12 198 299 655 6737 8304 10917 1609219367 20755 37690 13 351 916 926 18151 21708 23216 30321 33578 3405237949 14 54 332 373 2010 3332 5623 16301 34337 36451 37861 15 139 2571068 11090 20289 29694 29732 32640 35133 36404 16 457 885 968 2115 49565422 5949 17570 26673 32387 17 137 570 619 5006 6099 7979 14429 1665025443 32789 18 46 282 287 10258 18383 20258 27186 27494 28429 38266 19445 486 1058 1868 9976 11294 20364 23695 30826 35330 20 134 900 93112518 14544 17715 19623 21111 33868 34570 21 62 66 586 8020 20270 2383131041 31965 32224 35189 22 174 290 784 6740 14673 17642 26286 2738233447 34879 23 332 675 1033 1838 12004 15439 20765 31721 34225 38863 24527 558 832 3867 6318 8317 10883 13466 18427 25377 25 431 780 1021 11122873 7675 13059 17793 20570 20771 26 339 536 1015 5725 6916 10846 1448721156 28123 32614 27 456 830 1078 7511 11801 12362 12705 17401 2886734032 28 222 538 989 5593 6022 8302 14008 23445 25127 29022 29 37 393788 3025 7768 11367 22276 22761 28232 30394 30 234 257 1045 1307 29086337 26530 28142 34129 35997 31 35 46 978 9912 9978 12567 17843 2419434887 35206 32 39 959 967 5027 10847 14657 18859 28075 28214 36325 33275 477 823 11376 18073 28997 30521 31661 31941 32116 34 185 580 96611733 12013 12760 13358 19372 32534 35504 35 760 891 1046 11150 2035821638 29930 31014 33050 34840 36 360 389 1057 5316 5938 14186 1640432445 34021 35722 37 306 344 679 5224 6674 10305 18753 25583 30585 3694338 103 171 1016 8780 11741 12144 19470 20955 22495 27377 39 818 832 8943883 14279 14497 22505 28129 28719 31246 40 215 411 760 5886 25612 2855632213 32704 35901 36130 41 229 489 1067 2385 8587 20565 23431 2810230147 32859 42 288 664 980 8138 8531 21676 23787 26708 28798 34490 43 89552 847 6656 9889 23949 26226 27080 31236 35823 44 66 142 443 3339 38137977 14944 15464 19186 25983 45 605 876 931 16682 17669 25800 2822033432 35738 37382 46 346 423 806 5669 7668 8789 9928 19724 24039 2789347 48 460 1055 3512 7389 7549 20216 22180 28221 35437 48 187 636 6241678 4508 13588 19683 21750 30311 33480 49 25 768 935 2856 8187 905221850 29942 33217 34293 50 349 624 716 2698 6395 6435 8974 10649 1593217378 51 336 410 871 3582 9830 10885 13892 18027 19203 36659 52 176 8491078 17302 19379 27964 28164 28720 32557 35495 53 234 890 1075 9431 96059700 10113 11332 12679 24268 54 516 638 733 8851 19871 22740 25791 3015232659 35568 55 253 830 879 2086 16885 22952 23765 25389 34656 37293 5694 954 998 2003 3369 6870 7321 29856 31373 34888 57 79 350 933 4853 625211932 12058 21631 24552 24876 58 246 647 778 4036 10391 10656 1319432335 32360 34179 59 149 339 436 6971 8356 8715 11577 22376 28684 3124960 36 149 220 6936 18408 19192 19286 23063 28411 35312 61 273 683 10426327 10011 18041 21704 29097 30791 31425 62 46 138 722 2701 10984 1300219930 26625 28458 28965 63 12 1009 1040 1990 2930 5302 21215 22625 2301129288 64 125 241 819 2245 3199 8415 21133 26786 27226 38838 65 45 4761075 7393 15141 20414 31244 33336 35004 38391 66 432 578 667 1343 1046611314 11507 23314 27720 34465 67 248 291 556 1971 3989 8992 18000 1999823932 34652 68 68 694 837 2246 7472 7873 11078 12868 20937 35591 69 272924 949 2030 4360 6203 9737 19705 19902 38089 70 21 314 979 2311 26324109 19527 21920 31413 34277 71 197 253 804 1249 4315 10021 14358 2055927099 30525 72 9802 16164 17499 22378 22403 22704 26742 29908 73 906410904 12305 14057 16156 26000 32613 34536 74 5178 6319 10239 19343 2562830577 31110 32291

In another example, when the length N of the LDPC codeword is 16200 andthe code rate is 7/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 30 presented below:

TABLE 30 Indexes of rows where 1 is located in the 0th column i of theith column group  0 56 330 835 1133 1731 2171 5077 7762  1 21 259 8451827 2503 3258 7361 7490  2 105 779 1069 1366 7074 7251 7294 7514  3 16558 923 2455 4076 6294 7507 8475  4 37 197 384 2184 2223 6347 6525 7258 5 197 393 844 1961 3881 5842 6368 8032  6 374 588 1069 3093 4484 58687320  7 243 767 790 1603 1867 4804 7416  8 0 242 730 2141 4235 4642 5063 9 148 327 431 2291 3847 5133 7977 10 110 864 925 2730 4227 6604 7219 11571 746 867 1384 3974 5944 6713 12 268 347 948 1515 3629 5598 7538 13876 904 1049 4249 5198 6938 7701 14 690 748 782 1304 2117 4528 4589 1514 300 703 2968 4571 6102 7754 16 832 998 1071 2591 3865 4812 6321 17458 903 976 5179 5520 6862 8068 18 155 358 984 1417 1602 2697 3044 19312 701 784 1636 2183 3501 5170 20 85 981 989 2893 2951 4457 4685 215091 5244 5293 5404 6009 22 2171 2203 2344 3255 6338 23 3072 4338 69657045 8061

In another example, when the length N of the LDPC codeword is 64800 andthe code rate is 7/15, the indexes of rows where 1 is located in the0^(th) column of the ith column group in the matrix A and the matrix Care defined as shown in Table 31 presented below:

TABLE 31 Indexes of rows where 1 is located in the 0th column i of theith column group  0 460 792 1007 4580 11452 13130 26882 27020 32439  135 472 1056 7154 12700 13326 13414 16828 19102  2 45 440 772 4854 786326945 27684 28651 31875  3 744 812 892 1509 9018 12925 14140 21357 25106 4 271 474 761 4268 6706 9609 19701 19707 24870  5 223 477 662 1987 924718376 22148 24948 27694  6 44 379 786 8823 12322 14666 16377 28688 29924 7 104 219 562 5832 19665 20615 21043 22759 32180  8 41 43 870 796313718 14136 17216 30470 33428  9 592 744 887 4513 6192 18116 19482 2503234095 10 456 821 1078 7162 7443 8774 15567 17243 33085 11 151 666 9776946 10358 11172 18129 19777 32234 12 236 793 870 2001 6805 9047 1387730131 34252 13 297 698 772 3449 4204 11608 22950 26071 27512 14 202 428474 3205 3726 6223 7708 20214 25283 15 139 719 915 1447 2938 11864 1593221748 28598 16 135 853 902 3239 18590 20579 30578 33374 34045 17 9 13971 11834 13642 17628 21669 24741 30965 18 344 531 730 1880 16895 1758721901 28620 31957 19 7 192 380 3168 3729 5518 6827 20372 34168 20 28 521681 4313 7465 14209 21501 23364 25980 21 269 393 898 3561 11066 1198517311 26127 30309 22 42 82 707 4880 4890 9818 23340 25959 31695 23 189262 707 6573 14082 22259 24230 24390 24664 24 383 568 573 5498 1344913990 16904 22629 34203 25 585 596 820 2440 2488 21956 28261 28703 2959126 755 763 795 5636 16433 21714 23452 31150 34545 27 23 343 669 11593507 13096 17978 24241 34321 28 316 384 944 4872 8491 18913 21085 2319824798 29 64 314 765 3706 7136 8634 14227 17127 23437 30 220 693 899 879112417 13487 18335 22126 27428 31 285 794 1045 8624 8801 9547 19167 2189432657 32 386 621 1045 1634 1882 3172 13686 16027 22448 33 95 622 6932827 7098 11452 14112 18831 31308 34 446 813 928 7976 8935 13146 2711727766 33111 35 89 138 241 3218 9283 20458 31484 31538 34216 36 277 420704 9281 12576 12788 14496 15357 20585 37 141 643 758 4894 10264 1514416357 22478 26461 38 17 108 160 13183 15424 17939 19276 23714 26655 39109 285 608 1682 20223 21791 24615 29622 31983 40 123 515 622 7037 1394615292 15606 16262 23742 41 264 565 923 6460 13622 13934 23181 2547526134 42 202 548 789 8003 10993 12478 16051 25114 27579 43 121 450 5755972 10062 18693 21852 23874 28031 44 507 560 889 12064 13316 1962921547 25461 28732 45 664 786 1043 9137 9294 10163 23389 31436 34297 4645 830 907 10730 16541 21232 30354 30605 31847 47 203 507 1060 697112216 13321 17861 22671 29825 48 369 881 952 3035 12279 12775 1768217805 34281 49 683 709 1032 3787 17623 24138 26775 31432 33626 50 524792 1042 12249 14765 18601 25811 32422 33163 51 137 639 688 7182 816910443 22530 24597 29039 52 159 643 749 16386 17401 24135 28429 3346833469 53 107 481 555 7322 13234 19344 23498 26581 31378 54 249 389 5233421 10150 17616 19085 20545 32069 55 395 738 1045 2415 3005 3820 1954123543 31068 56 27 293 703 1717 3460 8326 8501 10290 32625 57 126 247 5156031 9549 10643 22067 29490 34450 58 331 471 1007 3020 3922 7580 2335828620 30946 59 222 542 1021 3291 3652 13130 16349 33009 34348 60 532 7191038 5891 7528 23252 25472 31395 31774 61 145 398 774 7816 13887 1493623708 31712 33160 62 88 536 600 1239 1887 12195 13782 16726 27998 63 151269 585 1445 3178 3970 15568 20358 21051 64 650 819 865 15567 1854625571 32038 33350 33620 65 93 469 800 6059 10405 12296 17515 21354 2223166 97 206 951 6161 16376 27022 29192 30190 30665 67 412 549 986 583310583 10766 24946 28878 31937 68 72 604 659 5267 12227 21714 32120 3347233974 69 25 902 912 1137 2975 9642 11598 25919 28278 70 420 976 10558473 11512 20198 21662 25443 30119 71 1 24 932 6426 11899 13217 1393516548 29737 72 53 618 988 6280 7267 11676 13575 15532 25787 73 111 739809 8133 12717 12741 20253 20608 27850 74 120 683 943 14496 15162 1544018660 27543 32404 75 600 754 1055 7873 9679 17351 27268 33508 76 344 7561054 7102 7193 22903 24720 27883 77 582 1003 1046 11344 23756 2749727977 32853 78 28 429 509 11106 11767 12729 13100 31792 79 131 555 9075113 10259 10300 20580 23029 80 406 915 977 12244 20259 26616 2789932228 81 46 195 224 1229 4116 10263 13608 17830 82 19 819 953 7965 999813959 30580 30754 83 164 1003 1032 12920 15975 16582 22624 27357 84 843311894 13531 17675 25889 31384 85 3166 3813 8596 10368 25104 29584 862466 8241 12424 13376 24837 32711

Hereinafter, positions of rows where 1 exists in the matrix A and thematrix C will be explained with reference to Table 24 by way of anexample.

Since the length N of the LDPC codeword is 16200 and the code rate is4/15 in Table 24, M₁=1080, M₂=10800, Q₁=3, and Q₂=30 in the parity checkmatrix 400 defined by Table 24 with reference to Table 22.

Herein, Q₁ is a size by which columns of the same column group arecyclic-shifted in the matrix A, and Q₂ is a size by which columns of thesame column group are cyclic-shifted in the matrix C.

In addition, Q₁=M₁/L, Q₂=M₂/L, M₁=g, and M₂=N−K−g, and L is an intervalat which a pattern of a column is repeated in the matrix A and thematrix C, and for example, may be 360.

The index of the row where 1 is located in the matrix A and the matrix Cmay be determined based on the M₁ value.

For example, since M₁=1080 in the case of Table 24, the positions of therows where 1 exists in the 0^(th) column of the ith column group in thematrix A may be determined based on values smaller than 1080 from amongthe index values of Table 24, and the positions of the rows where 1exists in the 0^(th) column of the ith column group in the matrix C maybe determined based on values greater than or equal to 1080 from amongthe index values of Table 24.

Specifically, in Table 24, the sequence corresponding to the 0^(th)column group is “19, 585, 710, 3241, 3276, 3648, 6345, 9224, 9890, and10841”. Accordingly, in the case of the 0^(th) column of the 0^(th)column group of the matrix A, 1 may be located in the 19^(th) row,585^(th) row, and 710^(th) row, and, in the case of the 0^(th) column ofthe 0^(th) column group of the matrix C, 1 may be located in the3241^(st) row, 3276^(th) row, 3648^(th) row, 6345^(th) row, 9224^(th)row, 9890^(th) row, and 10841^(st) row.

Once positions of 1 in the 0^(th) column of each column group of thematrix A are defined, positions of rows where 1 exists in another columnof each column group may be defined by cyclic-shifting from the previouscolumn by Q₁. Once positions of 1 in the 0^(th) column of each columngroup of the matrix C are defined, position of rows where 1 exists inanother column of each column group may be defined by cyclic-shiftingfrom the previous column by Q₂.

In the above-described example, in the case of the 0^(th) column of the0^(th) column group of the matrix A, 1 exists in the 19^(th) row,585^(th) row, and 710^(th) row. In this case, since Q₁=3, the indexes ofrows where 1 exists in the 1^(st) column of the 0^(th) column group are22(=19+3), 588(=585+3), and 713(=710+3), and the index of rows where 1exists in the 2^(nd) column of the 0^(th) column group are 25(=22+3),591 (=588+3), and 716(=713+3).

In the case of the 0^(th) column of the 0^(th) column group of thematrix C, 1 exists in the 3241^(st) row, 3276^(th) row, 3648^(th) row,6345^(th) row, 9224^(th) row, 9890^(th) row, and 10841^(st) row. In thiscase, since Q₂=30, the index of rows where 1 exists in the 1^(st) columnof the 0^(th) column group are 3271 (=3241+30), 3306(=3276+30), 3678(=3648+30), 6375 (=6345+30), 9254 (=9224+30), 9920 (=9890+30), and 10871(=10841+30), and the indexes of rows where 1 exists in the 2^(nd) columnof the 0^(th) column group are 3301 (=3271+30), 3336(=3306+30), 3708(=3678+30), 6405 (=6375+30), 9284 (=9254+30), 9950 (=9920+30), 10901(=10871+30).

In this method, the positions of rows where 1 exists in all columngroups of the matrix A and the matrix C are defined.

The matrix B may have a dual diagonal configuration, the matrix D mayhave a diagonal configuration (that is, the matrix D is an identitymatrix), and the matrix Z may be a zero matrix.

As a result, the parity check matrix 400 shown in FIG. 4 may be definedby the matrices A, B, C, D, and Z having the above-describedconfigurations.

Hereinafter, a method for performing LDPC encoding based on the paritycheck matrix 400 shown in FIG. 4 will be explained. An LDPC encodingprocess when the parity check matrix 400 is defined as shown in Table 24by way of an example will be explained for the convenience ofexplanation.

For example, when an information word block S=(s₀, s₁, . . . , S_(K−1))is LDPC-encoded, an LDPC codeword Λ=(λ₀, λ₁, . . . , λ_(N−1))=(s₀, s₁, .. . , S_(K−1), p₀, p₁, . . . , P_(M) ₁ _(+M) ₂ ⁻¹) including a paritybit P=(p₀, p₁, . . . , P_(M) ₁ _(+M) ₂ ⁻¹).

M₁ and M₂ indicate the size of the matrix B having the dual diagonalconfiguration and the size of the matrix C having the diagonalconfiguration, respectively, and M₁=g, M₂=N−K−g.

A process of calculating a parity bit is as follows. In the followingexplanation, the parity check matrix 400 is defined as shown in Table 24by way of an example, for the convenience of explanation.

Step 1) λ and p are initialized as λ_(i)=s_(i) (i=0, 1, . . . , K−1),p_(j)=0 (j=0, 1, . . . , M₁+M₂−1).

Step 2) The 0^(th) information word bit λ₀ is accumulated in the addressof the parity bit defined in the first row (that is, the row of i=0) ofTable 24. This may be expressed by Equation 12 presented below:

$\quad\begin{matrix}\begin{matrix}{P_{19} = {P_{19} \oplus \lambda_{0}}} & {P_{6345} = {P_{6345} \oplus \lambda_{0}}} \\{P_{585} = {P_{585} \oplus \lambda_{0}}} & {P_{9224} = {P_{9224} \oplus \lambda_{0}}} \\{P_{710} = {P_{710} \oplus \lambda_{0}}} & {P_{9890} = {P_{9890} \oplus \lambda_{0}}} \\{P_{3241} = {P_{3241} \oplus \lambda_{0}}} & {P_{10841} = {P_{10841} \oplus \lambda_{0}}} \\{P_{3276} = {P_{3276} \oplus \lambda_{0}}} & \; \\{P_{3648} = {P_{3648} \oplus \lambda_{0}}} & \;\end{matrix} & (12)\end{matrix}$

Step 3) Regarding the next L−1 number of information word bits λ_(m)(m=1, 2, . . . , L−1), λ_(m) is accumulated in the parity bit addresscalculated based on Equation 13 presented below:(χ+m×Q ₁) mod M ₁ (if χ<M ₁)M ₁+{(χ−M ₁ +m×Q ₂)mod M ₂} (if χ≥M ₁)  (13)

Herein, x is an address of a parity bit accumulator corresponding to the0^(th) information word bit λ₀.

In addition, Q₁=M₁/L and Q₂=M₂/L. In addition, since the length N of theLDPC codeword is 16200 and the code rate is 4/15 in Table 24, M₁=1080,M₂=10080, Q₁=3, Q₂=30, and L=360 with reference to Table 22.

Accordingly, an operation as shown in Equation 14 presented below may beperformed for the 1^(st) information word bit λ₁:

$\quad\begin{matrix}\begin{matrix}{P_{22} = {P_{22} \oplus \lambda_{1}}} & {P_{6375} = {P_{6375} \oplus \lambda_{1}}} \\{P_{588} = {P_{588} \oplus \lambda_{1}}} & {P_{9254} = {P_{9254} \oplus \lambda_{1}}} \\{P_{713} = {P_{713} \oplus \lambda_{1}}} & {P_{9920} = {P_{9920} \oplus \lambda_{1}}} \\{P_{3271} = {P_{3271} \oplus \lambda_{1}}} & {P_{10871} = {P_{10871} \oplus \lambda_{1}}} \\{P_{3306} = {P_{3306} \oplus \lambda_{1}}} & \; \\{P_{3678} = {P_{3678} \oplus \lambda_{1}}} & \;\end{matrix} & (14)\end{matrix}$

Step 4) Since the same address of the parity bit as in the second row(that is the row of i=1) of Table 24 is given to the Lth informationword bit λ_(L), in a similar method to the above-described method, theaddress of the parity bit regarding the next L−1 number of informationword bits λ_(m) (m=L+1, L+2, . . . , 2L−1) is calculated based onEquation 13. In this case, x is the address of the parity bitaccumulator corresponding to the information word bit λ_(L), and may beobtained based on the second row of Table 24.

Step 5) The above-described processes are repeated for L number of newinformation word bits of each group by considering new rows of Table 24as the address of the parity bit accumulator.

Step 6) After the above-described processes are repeated for thecodeword bits λ₀ to λ_(K−1), values regarding Equation 15 presentedbelow are calculated in sequence from i=1:P _(i) =P _(i) ⊕P _(i−1)(i=1,2, . . . M ₁−1)  (15)

Step 7) Parity bits λ_(K) to λ_(K+M) ₁ ⁻¹ corresponding to the matrix Bhaving the dual diagonal configuration are calculated based on Equation16 presented below:λ_(K+L×t+s) =p _(Q) ₁ _(×S+t)(0≤s<L,0≤t<Q ₁)  (16)

Step 8) The address of the parity bit accumulator regarding L number ofnew codeword bits λ_(K) to λ_(K+M) ₁ ⁻¹ of each group is calculatedbased on Table 24 and Equation 13.

Step 9) After the codeword bits λ_(K) to λ_(K+M) ₁ ⁻¹ are calculated,parity bits λ_(K+M) ₁ to λ_(K+M) ₁ _(+M) ₂ ⁻¹ corresponding to thematrix C having the diagonal configuration are calculated based onEquation 17 presented below:λ_(K+M) ₁ _(+L×t+s) =p _(M) ₁ _(+Q) ₂ _(×S+t)(0≤s<L,0≤t<Q ₂)  (17)

As a result, the parity bits may be calculated in the above-describedmethod.

Referring back to FIG. 1 , the encoder 110 may perform the LDPC encodingby using various code rates such as 3/15, 4/15, 5/15, 6/15, 7/15, 8/15,9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, the encoder 110 maygenerate an LDPC codeword having various lengths such as 16200, 64800,etc., based on the length of the information word bits and the coderate.

In this case, the encoder 110 may perform the LDPC encoding by using theparity check matrix, and the parity check matrix is configured as shownin FIGS. 2 to 4 .

In addition, the encoder 110 may perform Bose, Chaudhuri, Hocquenghem(BCH) encoding as well as LDPC encoding. To achieve this, the encoder110 may further include a BCH encoder (not shown) to perform BCHencoding.

In this case, the encoder 110 may perform encoding in an order of BCHencoding and LDPC encoding. Specifically, the encoder 110 may add BCHparity bits to input bits by performing BCH encoding and LDPC-encodesthe information word bits including the input bits and the BCH paritybits, thereby generating the LDPC codeword.

The interleaver 120 interleaves the LDPC codeword. That is, theinterleaver 120 receives the LDPC codeword from the encoder 110, andinterleaves the LDPC codeword based on various interleaving rules.

In particular, the interleaver 120 may interleave the LDPC codeword suchthat a bit included in a predetermined bit group from among a pluralityof bit groups constituting the LDPC codeword (that is, a plurality ofgroups or a plurality of blocks) is mapped onto a predetermined bit of amodulation symbol.

In this case, the interleaver 120 may interleave the LDPC codeword suchthat bits included in continuous bit groups from among the plurality ofbit groups of the LDPC codeword are mapped onto the same modulationsymbol.

In addition, when check nodes connected only to a single parity bit inthe parity check matrix of the LDPC code exists in plurality number, theinterleaver 120 may interleave the LDPC codeword such that bits includedin the bit groups corresponding to the parity bit to which the checknodes are connected are selectively mapped onto the modulation symbol.

Accordingly, the modulator 130 may map the bit included in thepredetermined bit group from among the plurality of bit groups of theLDPC codeword onto a predetermined bit of the modulation symbol.

That is, the modulator 130 may map the bits included in the continuousbit groups from among the plurality of bit groups of the LDPC codewordonto the same modulation symbol. In addition, when the check nodesconnected only to a single parity bit in the parity check matrix of theLDPC code exists in plurality number, the modulator 130 may selectivelymap the bits included in the bit groups corresponding to the parity bitto which the check nodes are connected onto the same modulation symbol.

To achieve this, as shown in FIG. 5 , the interleaver 120 may include aparity interleaver 121, a group interleaver (or a group-wise interleaver122), a group twist interleaver 123 and a block interleaver 124.

The parity interleaver 121 interleaves the parity bits constituting theLDPC codeword.

Specifically, when the LDPC codeword is generated based on the paritycheck matrix 200 having the configuration of FIG. 2 , the parityinterleaver 121 may interleave only the parity bits of the LDPC codewordby using Equations 18 presented below:u _(i) =c _(i) for 0≤i<K _(ldpc), andu _(K) _(ldpc) _(+M·t+s) c _(K) _(ldpc) _(+Q) _(ldpc) _(·s+t) for0≤s<M,0≤t<Q _(ldpc)  (18),

where M is an interval at which a pattern of a column group is repeatedin the information word submatrix 210, that is, the number of columnsincluded in a column group (for example, M=360), and Q_(ldpc) is a sizeby which each column is cyclic-shifted in the information word submatrix210. That is, the parity interleaver 121 performs parity interleavingwith respect to the LDPC codeword c=(c₀, c₁, . . . , c_(N) _(ldpc) ⁻¹),and outputs U=(u₀, u₁, . . . , u_(N) _(ldpc) ⁻¹).

The LDPC codeword parity-interleaved in the above-described method maybe configured such that a predetermined number of continuous bits of theLDPC codeword have similar decoding characteristics (cycle distribution,a degree of a column, etc.).

For example, the LDPC codeword may have the same characteristics on thebasis of M number of continuous bits. Herein, M is an interval at whicha pattern of a column group is repeated in the information wordsubmatrix 210 and, for example, may be 360.

Specifically, a product of the LDPC codeword bits and the parity checkmatrix should be “0”. This means that a sum of products of the i^(th)LDPC codeword bit, c_(i) (i=0, 1, . . . , N_(ldpc)−1) and the i^(th)column of the parity check matrix should be a “0” vector. Accordingly,the i^(th) LDPC codeword bit may be regarded as corresponding to thei^(th) column of the parity check matrix.

In the case of the parity check matrix 200 of FIG. 2 , M number ofcolumns in the information word submatrix 210 belong to the same groupand the information word submatrix 210 has the same characteristics onthe basis of a column group (for example, the columns belonging to thesame column group have the same degree distribution and the same cyclecharacteristic).

In this case, since M number of continuous bits in the information wordbits correspond to the same column group of the information wordsubmatrix 210, the information word bits may be formed of M number ofcontinuous bits having the same codeword characteristics. When theparity bits of the LDPC codeword are interleaved by the parityinterleaver 121, the parity bits of the LDPC codeword may be formed of Mnumber of continuous bits having the same codeword characteristics.

However, regarding the LDPC codeword encoded based on the parity checkmatrix 300 of FIG. 3 and the parity check matrix 400 of FIG. 4 , parityinterleaving may not be performed. In this case, the parity interleaver121 may be omitted.

The group interleaver 122 may divide the parity-interleaved LDPCcodeword into a plurality of bit groups and rearrange the order of theplurality of bit groups in bit group wise (or bit group unit). That is,the group interleaver 122 may interleave the plurality of bit groups inbit group wise.

According to an exemplary embodiment, when the parity interleaver 121 isomitted, the group interleaver 122 may divide the LDPC codeword into aplurality of bit groups and rearrange the order of the plurality of bitgroups in bit group wise.

To achieve this, the group interleaver 122 divides theparity-interleaved LDPC codeword into a plurality of bit groups by usingEquation 19 or Equation 20 presented below.

$\begin{matrix}{X_{j} = {{\left\{ {{\left. u_{k} \middle| j \right. = \left\lfloor \frac{k}{360} \right\rfloor},{0 \leq k < N_{ldpc}}} \right\}\mspace{14mu}{for}\mspace{14mu} 0} \leq j < N_{group}}} & (19) \\{{X_{j} = \left\{ {\left. u_{k} \middle| {{360 \times j} \leq k < {360 \times \left( {j + 1} \right)}} \right.,{0 \leq k < N_{ldpc}}} \right\}}{{{{for}\mspace{14mu} 0} \leq j < N_{group}},}} & (20)\end{matrix}$where N_(group) is the total number of bit groups, X_(j) is the j^(th)bit group, and u_(k) is the k^(th) LDPC codeword bit input to the groupinterleaver 122. In addition,

$\left\lfloor \frac{k}{360} \right\rfloor$is the largest integer below k/360.

Since 360 in these equations indicates an example of the interval M atwhich the pattern of a column group is repeated in the information wordsubmatrix, 360 in these equations can be changed to M.

The LDPC codeword which is divided into the plurality of bit groups maybe as shown in FIG. 6 .

Referring to FIG. 6 , the LDPC codeword is divided into the plurality ofbit groups and each bit group is formed of M number of continuous bits.When M is 360, each of the plurality of bit groups may be formed of 360bits. Accordingly, the bit groups may be formed of bits corresponding tothe column groups of the parity check matrix.

Specifically, since the LDPC codeword is divided by M number ofcontinuous bits, K_(ldpc) number of information word bits are dividedinto (K_(ldpc)/M) number of bit groups and N_(ldpc)−K_(ldpc) number ofparity bits are divided into (N_(ldpc)−K_(ldpc))/M number of bit groups.Accordingly, the LDPC codeword may be divided into (N_(ldpc)/M) numberof bit groups in total.

For example, when M=360 and the length N_(ldpc) of the LDPC codeword is64800, the number of bit groups N_(groups) is 180(=64800/360), and, whenthe M=360 and the length N_(ldpc) of the LDPC codeword is 16200, thenumber of bit groups N_(group) is 45(=16200/360).

As described above, the group interleaver 122 divides the LDPC codewordsuch that M number of continuous bits are included in a same group sincethe LDPC codeword has the same codeword characteristics on the basis ofM number of continuous bits. Accordingly, when the LDPC codeword isgrouped by M number of continuous bits, the bits having the samecodeword characteristics belong to the same group.

In the above-described example, the number of bits constituting each bitgroup is M. However, this is merely an example and the number of bitsconstituting each bit group is variable.

For example, the number of bits constituting each bit group may be analiquot part of M. That is, the number of bits constituting each bitgroup may be an aliquot part of the number of columns constituting acolumn group of the information word submatrix of the parity checkmatrix. In this case, each bit group may be formed of aliquot part of Mnumber of bits. For example, when the number of columns constituting acolumn group of the information word submatrix is 360, that is, M=360,the group interleaver 122 may divide the LDPC codeword into a pluralityof bit groups such that the number of bits constituting each bit groupis one of the aliquot parts of 360.

In the following explanation, the number of bits constituting a bitgroup is M by way of an example, for the convenience of explanation.

Thereafter, the group interleaver 122 interleaves the LDPC codeword inbit group wise. Specifically, the group interleaver 122 may group theLDPC codeword into the plurality of bit groups and rearrange theplurality of bit groups in bit group wise. That is, the groupinterleaver 122 changes positions of the plurality of bit groupsconstituting the LDPC codeword and rearranges the order of the pluralityof bit groups constituting the LDPC codeword in bit group wise.

Herein, the group interleaver 122 may rearrange the order of theplurality of bit groups in bit group wise such that bit groups includingbits mapped onto the same modulation symbol from among the plurality ofbit groups are spaced apart from one another at predetermined intervals.

In this case, the group interleaver 122 may rearrange the order of theplurality of bit groups in bit group wise by considering at least one ofthe number of rows and columns of the block interleaver 124, the numberof bit groups of the LDPC codeword, and the number of bits included ineach bit group, such that bit groups including bits mapped onto the samemodulation symbol are spaced apart from one another at predeterminedintervals.

To achieve this, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bit group wise by using Equation 21presented below:Y _(j) =X _(π(j))(0≤j<N _(group))  (21),

where X_(j) is the j^(th) bit group before group interleaving, and Y_(j)is the j^(th) bit group after group interleaving. In addition, π(j) is aparameter indicating an interleaving order and is determined by at leastone of a length of an LDPC codeword, a modulation method, and a coderate. That is, π(j) denotes a permutation order for group wiseinterleaving.

Accordingly, X_(π(j)) is a π(j)^(th) bit group before groupinterleaving, and Equation 21 means that the pre-interleaving π(j)^(th)bit group is interleaved into the j^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be definedas in Tables 32 to 56 presented below.

In this case, π(j) is defined according to a length of an LPDC codewordand a code rate, and a parity check matrix is also defined according toa length of an LDPC codeword and a code rate. Accordingly, when LDPCencoding is performed based on a specific parity check matrix accordingto a length of an LDPC codeword and a code rate, the LDPC codeword maybe interleaved in bit group wise based on π(j) satisfying thecorresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rateof 7/15 to generate an LDPC codeword of a length of 16200, the groupinterleaver 122 may perform interleaving by using π(j) which is definedaccording to the length of the LDPC codeword of 16200 and the code rateof 7/15 in Tables 32 to 56 presented below.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, thecode rate is 5/15, and the modulation method (or modulation format) isQuadrature Phase Shift Keying (QPSK), π(j) may be defined as in Table 32presented below. In particular, Table 32 may be applied when LDPCencoding is performed based on the parity check matrix defined by Table26.

TABLE 32 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 35 7 29 11 14 32 38 2820 17 25 39 19 4 1 12 10 30 0 44 43 2 21 Group-wise 5 13 34 37 23 15 3618 42 16 33 31 27 22 3 6 40 24 41 9 26 8 interleaver input

In the case of Table 32, Equation 21 may be expressed asY₀=X_(π(0))=X₃₅, Y₁=X_(π(1))=X₇, Y₂=X_(π(2))=X₂₉, . . . ,Y₄₃=X_(π(43))=X₂₆, and Y₍₄₄₎=X_(π(44))=X₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 35^(th) bit group to the 0^(th) bitgroup, the 7^(th) bit group to the 1^(st) bit group, the 29^(th) bitgroup to the 2^(nd) bit group, . . . , the 26^(th) bit group to the43^(rd) bit group, and the 8^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and the modulation method is QPSK, π(j)may be defined as in Table 33 presented below. In particular, Table 33may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 6.

TABLE 33 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 4 22 23 44 34 1 3 2 3242 6 15 30 40 18 5 28 38 7 14 26 36 9 Group-wise 0 16 43 33 17 11 12 3141 21 20 29 39 10 24 27 37 13 19 25 35 8 interleaver input

In the case of Table 33, Equation 21 may be expressed as Y₀=X_(π(0))=X₄,Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, andY₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group tothe 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . .. , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and the modulation method is QPSK, π(j)may be defined as in Table 34 presented below. In particular, Table 34may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 8.

TABLE 34 j-th block of Order of bits group to be block interleavedGroup-wise π(j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 12 1314 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 34 3536 37 38 39 40 41 42 43 44 π(j)-th block of 28 16 13 42 32 22 14 20 3626 6 4 40 30 8 9 44 34 24 10 17 38 27 Group-wise 12 19 41 31 21 1 15 3525 2 0 39 29 3 5 43 33 23 7 11 37 18 interleaver input

In the case of Table 34, Equation 21 may be expressed asY₀=X_(π(0))=X₂₈, Y₁=X_(π(1))=X₁₆, Y₂=X_(π(2))=X₁₃, Y₄₃=X_(π(43))=X₃₇,and Y₄₄=X_(π(44))=X₁₈. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bit group wise bychanging the 28^(th) bit group to the 0^(th) bit group, the 16^(th) bitgroup to the 1^(st) bit group, the 13^(th) bit group to the 2^(nd) bitgroup, . . . , the 37^(th) bit group to the 43^(rd) bit group, and the18^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 11/15, and the modulation method is QPSK, π(j)may be defined as in Table 35 presented below. In particular, Table 35may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 10.

TABLE 35 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 1 2 40 14 27 24 36 7 911 12 42 18 17 28 38 31 5 32 34 44 23 0 Group-wise 25 39 26 10 29 35 815 16 13 41 3 6 4 37 19 22 20 33 43 30 21 interleaver input

In the case of Table 35, Equation 21 may be expressed as Y₀=X_(π(0))=X₁,Y₁=X_(π(1))=X₂, Y₂=X_(π(2))=X₄₀, . . . , Y₄₃=X_(π(43))=X₃₀, andY₄₄=X_(π(44))=X₂₁. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 1^(st) bit group to the 0^(th) bit group, the 2^(nd) bit group tothe 1^(st) bit group, the 40^(th) bit group to the 2^(nd) bit group, . .. , the 30^(th) bit group to the 43^(rd) bit group, and the 21^(st) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 13/15, and the modulation method is QPSK, π(j)may be defined as in Table 36 presented below. In particular, Table 36may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 12.

TABLE 36 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 26 10 12 38 28 15 0 4434 24 14 8 40 30 20 13 42 32 22 11 9 36 25 Group-wise 7 5 37 27 4 16 4333 23 2 18 39 29 19 6 41 31 21 3 17 35 1 interleaver input

In the case of Table 36, Equation 21 may be expressed asY₀=X_(π(0))=X₂₆, Y₁=X_(π(1))=X₁₀, Y₂=X_(π(2))=X₁₂, Y₄₃=X_(π(43))=X₃₅,and Y₄₄=X_(π(44))=X₁. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bit group wise bychanging the 26^(th) bit group to the 0^(th) bit group, the 10^(th) bitgroup to the 1^(st) bit group, the 12^(th) bit group to the 2^(nd) bitgroup, . . . , the 35^(th) bit group to the 43^(rd) bit group, and the1^(st) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 5/15, and the modulation method is QPSK, π(j)may be defined as in Table 37 presented below. In particular, Table 37may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 4.

TABLE 37 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 5 20 30 40 12 18 28 38 17 24 34 44 2 22 32 42 10 8 26 36 14 13 Group-wise 19 29 39 9 17 27 37 153 23 33 43 16 21 31 41 0 4 25 35 11 6 interleaver input

In the case of Table 37, Equation 21 may be expressed as Y₀=X_(π(0))=X₅,Y₁=X_(π(1))=X₂₀, Y₂=X_(π(2))=X₃₀, . . . , Y₄₃=X_(π(43))=X₁₁, andY₄₄=X_(π(44))=X₆. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 5^(th) bit group to the 0^(th) bit group, the 20^(th) bit group tothe 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . .. , the 11^(th) bit group to the 43^(rd) bit group, and the 6^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and the modulation method is QPSK, π(j)may be defined as in Table 38 presented below. In particular, Table 38may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 5.

TABLE 38 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 26 10 12 38 28 15 0 4434 24 14 8 40 30 20 13 42 32 22 11 9 36 25 Group-wise 7 5 37 27 4 16 4333 23 2 18 39 29 19 6 41 31 21 3 17 35 1 interleaver input

In the case of Table 38, Equation 21 may be expressed asY₀=X_(π(0))=X₂₆, Y₁=X_(π(1))=X₁₀, Y₂=X_(π(2))=X₁₂, . . . ,Y₄₃=X_(π(43))=X₃₅, and Y₄₄=X_(π(44))=X₁. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 26^(th) bit group to the 0^(th) bitgroup, the 10^(th) bit group to the 1^(st) bit group, the 12^(th) bitgroup to the 2^(nd) bit group, . . . , the 35^(th) bit group to the43^(rd) bit group, and the 1^(st) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and the modulation method is QPSK, π(j)may be defined as in Table 39 presented below. In particular, Table 39may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 7.

TABLE 39 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 4 22 23 44 34 1 3 2 3242 6 15 30 40 18 5 28 38 7 14 26 36 9 Group-wise 0 16 43 33 17 11 12 3141 21 20 29 39 10 24 27 37 13 19 25 35 8 interleaver input

In the case of Table 39, Equation 21 may be expressed as Y₀₌X_(π(0))=X₄,Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, andY₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group tothe 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . .. , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 11/15, and the modulation method is QPSK, π(j)may be defined as in Table 40 presented below. In particular, Table 40may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 9.

TABLE 40 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 4 22 23 44 34 1 3 2 3242 6 15 30 40 18 5 28 38 7 14 26 36 9 Group-wise 0 16 43 33 17 11 12 3141 21 20 29 39 10 24 27 37 13 19 25 35 8 interleaver input

In the case of Table 40, Equation 21 may be expressed as Y₀=X_(π(0))=X₄,Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, andY₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group tothe 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . .. , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 13/15, and the modulation method is QPSK, π(j)may be defined as in Table 41 presented below. In particular, Table 41may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 11.

TABLE 41 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 6 3 30 40 9 11 28 38 227 24 34 44 13 8 32 42 1 12 26 36 0 10 Group-wise 15 29 39 17 19 27 37 24 23 33 43 20 21 31 41 14 18 25 35 16 5 interleaver input

In the case of Table 41, Equation 21 may be expressed as Y₀=X₇₀)=X₆,Y₁=X_(π(1))=X₃, Y₂=X_(π(2))=X₃₀, . . . , Y₄₃=X_(π(43))=X₁₆, andY₄₄=X_(π(44))=X₅. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 6^(th) bit group to the 0^(th) bit group, the 3^(rd) bit group tothe 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . .. , the 16^(th) bit group to the 43^(rd) bit group, and the 5^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and the modulation method is QPSK, π(j)may be defined as in Table 42 presented below. In particular, Table 42may be applied when LDPC encoding is performed based on the parity checkmatrix defined by Table 6.

TABLE 42 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 3 22 7 18 6 1 4 14 5 152 23 26 28 30 32 34 36 10 38 21 44 9 Group-wise 0 33 40 42 17 11 19 2420 12 16 25 27 29 31 13 35 37 39 41 43 8 interleaver input

In the case of Table 42, Equation 21 may be expressed as Y₀=X_(π(0))=X₃,Y₁=X_(π(1))X₂₂,Y₂=X_(π(2))=X₇, . . . , Y₄₃=X_(π(43))=X₄₃, andY₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrangethe order of the plurality of bit groups in bit group wise by changingthe 3^(rd) bit group to the 0^(th) bit group, the 22^(nd) bit group tothe 1^(st) bit group, the 7^(th) bit group to the 2^(nd) bit group, . .. , the 43^(rd) bit group to the 43^(rd) bit group, and the 8^(th) bitgroup to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 5/15, and the modulation method is QPSK, π(j)may be defined as in Table 43 presented below.

TABLE 43 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 28 20 8 39 21 25 22 1729 38 15 7 43 24 11 35 30 27 14 10 6 9 13 Group-wise 42 40 23 36 31 3 341 41 2 18 44 19 0 37 26 12 32 4 33 16 5 interleaver input

In the case of Table 43, Equation 21 may be expressed asY₀=X_(π(0))=X₂₈, Y₁=X_(π(0))=X₂₀, Y₂=X_(π(2))=X₈, . . . ,Y₄₃=X_(π(43))=X₁₆, and Y₄₄=X_(π(44))=X₅. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 28^(th) bit group to the 0^(th) bitgroup, the 20^(th) bit group to the 1^(st) bit group, the 8^(th) bitgroup to the 2^(nd) bit group, . . . , the 16^(th) bit group to the43^(rd) bit group, and the 5^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 44 presented below.

TABLE 44 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 36 2 31 18 13 6 40 43 2926 22 41 12 25 34 35 30 3 20 27 44 37 39 Group-wise 1 33 24 28 5 42 1721 15 9 38 32 10 23 7 0 11 19 14 8 4 16 interleaver input

In the case of Table 44, Equation 21 may be expressed asY₀=X_(π(0))=X₃₆, Y₁=X_(π(1))=X₂, Y₂=X_(π(2))=X₃₁, . . . ,Y₄₃=X_(π(43))=X₄, and Y₄₄=X_(π(44))=X₁₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 36^(th) bit group to the 0^(th) bitgroup, the 2^(nd) bit group to the 1^(st) bit group, the 31^(st) bitgroup to the 2^(nd) bit group, . . . , the 4^(th) bit group to the43^(rd) bit group, and the 16^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 7/15, and the modulation method is QPSK, π(j)may be defined as in Table 45 presented below.

TABLE 45 j th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 12 39 21 17 11 0 24 2616 40 22 5 36 20 41 32 33 19 44 7 15 23 30 Group-wise 43 9 14 4 8 25 635 37 13 29 10 1 18 28 38 42 31 3 27 34 2 interleaver input

In the case of Table 45, Equation 21 may be expressed asY₀=X_(π(0))=X₁₂, Y₁=X_(π(1))=X₃₉, Y₂=X_(π(2))=X₂₁, . . . ,Y₄₃=X_(π(43))=X₃₄, and Y₄₄=X_(π(44))=X₂. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 12^(th) bit group to the 0^(th) bitgroup, the 39^(th) bit group to the 1^(st) bit group, the 21^(st) bitgroup to the 2^(nd) bit group, . . . , the 34^(th) bit group to the43^(rd) bit group, and the 2^(nd) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is16200, the code rate is 9/15, and the modulation method is QPSK, π(j)may be defined as in Table 46 presented below.

TABLE 46 j-th block of Order of bits group to be block interleavedGroup-wise π (j) (0 ≤ j < 45) interleaver 0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 19 20 21 22 output 23 24 25 26 27 28 29 30 31 32 33 3435 36 37 38 39 40 41 42 43 44 π (j)-th block of 41 37 26 22 32 9 23 21 84 25 15 10 17 19 16 2 6 36 3 30 24 1 Group-wise 29 13 5 0 34 27 42 12 3343 28 35 40 14 44 11 18 7 31 20 39 38 interleaver input

In the case of Table 46, Equation 21 may be expressed asY₀=X_(π(0))=X₄₁, Y₁=X_(π(1))=X₃₇, Y₂=X_(π(2))=X₂₆, . . . ,Y₄₃=X_(π(43))X₃₉, and Y₄₄=X_(π(44))=X₃₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 41^(st) bit group to the 0^(th) bitgroup, the 37^(th) bit group to the 1^(st) bit group, the 26^(th) bitgroup to the 2^(nd) bit group, . . . , the 39^(th) bit group to the43^(rd) bit group, and the 38^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 5/15, and the modulation method is QPSK, π(j)may be defined as in Table 47 presented below.

TABLE 47 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 145 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 120 75 171 13 147 56 97 134 41 87 160 23 109 2 17877 62 148 130 50 96 34 18 Group-wise 115 4 159 81 169 71 136 149 94 3921 110 121 60 8 174 73 131 142 157 40 24 107 interleaver 86 117 3 54 68175 140 154 164 16 28 100 82 42 119 65 179 143 132 5 17 162 104 input,92 52 76 118 176 27 66 38 151 1 138 103 91 128 116 51 26 170 11 36 67145 79 98 127 112 155 48 25 173 15 64 137 37 84 126 95 153 74 105 163 758 47 31 141 129 89 19 152 72 106 165 59 6 46 33 133 85 177 146 122 2269 167 0 111 55 99 45 12 32 83 125 139 158 70 168 57 113 102 44 30 88123 20 9 78 166 61 144 101 49 456 35 124 114 10 90 172 63 135 80 53 15029 43 108 14 93 161

In the case of Table 47, Equation 21 may be expressed asY₀=X_(π(0))=X₁₂₀, Y₁X_(π(1))=X₇₅, Y₂X_(π(2))=X₁₇₁, . . . ,Y₁₇₈=X_(π(178))X₉₃, and Y₁₇₉=X_(π(179))=X₁₆₁. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 120^(th) bit group to the 0^(th) bitgroup, the 75^(th) bit group to the 1^(st) bit group, the 171^(st) bitgroup to the 2^(nd) bit group, . . . , the 93^(rd) bit group to the178^(th) bit group, and the 161^(st) bit group to the 179^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 48 presented below.

TABLE 48 Order of bits group to be block interleaved π(j) (0 < j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 92 79 168 44 15 63 147 109 157 26 136 94 124 2 4214 64 176 105 155 52 144 86 Group-wise 116 133 24 38 65 9 167 102 156 53177 112 128 28 76 45 142 4 89 99 60 175 153 interleaver 118 35 19 129 46139 6 81 70 179 151 95 57 18 115 30 169 41 135 78 125 148 104 input, 6216 91 29 161 40 3 174 51 73 123 113 61 84 97 13 34 138 172 158 0 23 7147 59 83 117 98 134 146 170 7 159 27 69 43 88 58 101 121 140 17 111 1178 75 166 87 37 54 126 150 12 22 114 103 72 160 82 93 50 171 33 137 14911 107 127 21 77 96 66 162 36 48 145 10 108 119 25 131 85 67 163 173 49141 39 106 152 5 122 90 20 74 164 56 132 32 110 143 100 8 120 154 80 6853 130 31 165

In the case of Table 48, Equation 21 may be expressed asY₀=X_(π(0))=X₉₂, Y₁=X_(π(1))=X₇₉, Y₂X_(π(2))=X₁₆₈, . . . ,Y₁₇₈=X_(π(178))=X₃₁, and Y₁₇₉=X_(π(179))=X₁₆₅. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 92^(nd) bit group to the 0^(th) bitgroup, the 79^(th) bit group to the 1^(st) bit group, the 168^(th) bitgroup to the 2^(nd) bit group, . . . , the 31^(st) bit group to the178^(th) bit group, and the 165^(th) bit group to the 179^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 49 presented below.

TABLE 49 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 53 65 29 159 39 13 134 148 108 120 85 174 75 54 1641 21 44 95 130 144 118 154 Group-wise 33 76 58 106 167 11 96 0 23 136151 177 78 60 42 122 165 102 92 12 24 147 179 interleaver 82 67 52 38117 105 135 94 160 27 171 2 146 17 69 49 123 37 110 133 158 87 173input, 98 8 19 57 72 121 36 132 149 86 176 100 7 26 59 73 166 47 112 15384 141 99 4 31 131 64 16 172 119 109 48 83 143 3 157 93 30 129 169 61103 15 113 71 142 43 456 89 32 5 168 124 56 104 77 138 18 152 114 178 46163 28 62 125 81 6 91 139 107 150 41 162 25 66 175 79 14 55 126 115 14035 45 90 68 101 161 9 80 22 128 111 145 50 34 70 97 170 155 10 20 127116 137 51 40 74 63 88

In the case of Table 49, Equation 21 may be expressed asY₀=X_(π(0))=X₅₃, Y₁=X_(π(1))=X₆₅, Y₂=X_(π(2))=X₂₉, Y₁₇₈=X_(π(178))=X₆₃,and Y₁₇₉=X_(π(179))=X₈₈. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bit group wise bychanging the 53^(rd) bit group to the 0^(th) bit group, the 65^(th) bitgroup to the 1^(st) bit group, the 29^(th) bit group to the 2^(nd) bitgroup, . . . , the 63^(rd) bit group to the 178^(th) bit group, and the88^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 50 presented below.

TABLE 50 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56 16743 32 128 156 112 4 89 of 140 69 14 100 49 34 168 151 120 0 89 110 13664 13 74 45 170 160 125 149 91 111 Group-wise 2 139 55 67 41 21 161 7731 121 173 104 5 143 58 94 44 159 84 71 116 16 27 interleaver 6 133 57106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 76input, 96 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 12336 152 80 66 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10126 48 165 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98109 22 75 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29102 92 68 141 81 46

In the case of Table 50, Equation 21 may be expressed asY₀=X_(π(0))=X₁₈, Y₁X_(π(1))X₁₆₉, Y₂X_(π(2))X₃₀, . . . ,Y₁₇₈=X_(π(178))X₈₁, and Y₇₉X_(π(179))=X₄₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 18^(th) bit group to the 0^(th) bitgroup, the 169^(th) bit group to the 1^(st) bit group, the 30^(th) bitgroup to the 2^(nd) bit group, . . . , the 81^(st) bit group to the178^(th) bit group, and the 46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 51 presented below.

TABLE 51 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56 16743 32 128 156 112 4 89 of 140 69 14 100 49 34 168 151 120 0 86 110 13664 13 74 45 170 160 125 149 91 111 Group-wise 2 139 55 67 41 21 161 7731 121 173 104 5 143 58 94 44 159 84 71 116 16 27 interleaver 6 133 57106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 76input, 96 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 12336 152 80 66 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10126 48 165 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98109 22 75 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29102 92 68 141 81 46

In the case of Table 51, Equation 21 may be expressed asY₀=X_(π(0))=X₁₈, Y₁=X_(π(1))=X₁₆₉, Y₂=X_(π(2))=X₃₀, . . . ,Y₁₇₈=X_(π(178))=X₈₁, and Y₁₇₉=X_(π(179))=X₄₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 18^(th) bit group to the 0^(th) bitgroup, the 169^(th) bit group to the 1^(st) bit group, the 30^(th) bitgroup to the 2^(nd) bit group, . . . , the 81^(st) bit group to the178^(th) bit group, and the 46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 52 presented below.

TABLE 52 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56167 43 32 128 156 112 4 89 Group-wise 140 69 14 100 49 34 168 151 120 086 110 136 64 13 74 45 170 160 125 149 91 111 interleaver 2 139 55 67 4121 161 77 31 121 173 104 5 143 58 94 44 159 84 71 116 16 27 input, 6 13357 106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 7696 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 123 36 15280 66 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10 126 48165 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98 109 2275 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29 102 9268 141 81 46

In the case of Table 52, Equation 21 may be expressed asY₀=X_(π(0))=X₁₈, Y₁=X_(π(1))=X₁₆₉, Y₂=X_(π(2))=X₃₀, Y₁₇₈=X_(π(178))=X₈₁,and Y₁₇₉=X_(π(179))=X₄₆. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bit group wise bychanging the 18^(th) bit group to the 0^(th) bit group, the 169^(th) bitgroup to the 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bitgroup, . . . , the 81^(st) bit group to the 178^(th) bit group, and the46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 53 presented below.

TABLE 53 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 43 150 26 119 108 7 173 163 81 135 71 45 153 55 92125 16 115 32 177 105 67 140 Group-wise 79 54 4 126 154 20 166 37 112 9564 144 76 48 5 134 124 25 160 176 88 59 100 interleaver 74 47 1 12 127137 36 178 90 162 22 147 117 72 101 2 132 33 52 84 157 172 21 input, 14373 113 98 131 40 60 83 3 167 18 50 149 109 28 93 130 120 65 0 161 175 4415 77 148 104 91 114 66 133 165 29 46 56 17 152 105 86 122 6 75 170 13831 42 62 151 106 85 121 10 96 168 139 24 34 53 179 158 107 69 8 123 8797 141 38 169 23 57 156 111 13 70 80 99 128 35 145 171 49 155 110 11 6182 94 129 39 27 142 174 159 116 51 14 63 78 89 103 30 41 136 164 146 11819 68 9 58

In the case of Table 53, Equation 21 may be expressed asY₀=X_(π(0))=X₄₃, Y₁=X₇(1)=X₁₅₀, Y₂=X_(π(2))=X₂₆, . . . ,Y₁₇₈=X_(π(178))=X₉, and Y₁₇₉=X_(π(179))=X₅₈. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 43^(rd) bit group to the 0^(th) bitgroup, the 150^(th) bit group to the 1^(st) bit group, the 26^(th) bitgroup to the 2^(nd) bit group, . . . , the 9^(th) bit group to the178^(th) bit group, and the 58^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 54 presented below.

TABLE 54 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 108 178 95 30 159 120 11 45 71 57 137 82 149 174 9633 117 127 160 19 67 52 0 Group-wise 81 179 141 102 37 115 128 163 63 12151 85 177 27 97 42 73 138 166 62 107 125 156 interleaver 15 25 89 17640 51 145 77 114 61 99 162 28 129 7 17 39 152 86 74 140 53 175 input,101 123 2 13 31 165 88 155 143 41 59 110 132 70 9 24 171 91 122 146 4836 106 161 136 14 75 60 94 173 3 119 47 148 109 29 133 84 16 66 167 6121 49 157 104 26 144 134 93 72 169 1 38 55 116 103 18 153 142 83 126 658 172 50 32 100 21 111 154 78 139 124 68 168 90 56 35 4 22 150 113 13546 79 69 98 164 58 34 5 147 118 23 44 130 80 92 105 64 170 54 10 158 2043 131 76 87 112

In the case of Table 54, Equation 21 may be expressed asY₀=X_(π(0))=X₁₀₈, Y₁=X_(π(1))=X₁₇₈, Y₂X_(π(2))=X₉₅, . . . ,Y₁₇₈=X_(π(178))X₈₇, and Y₁₇₉=X_(π(179))=X₁₁₂. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 108^(th) bit group to the 0^(th) bitgroup, the 178^(th) bit group to the 1^(st) bit group, the 95^(th) bitgroup to the 2^(nd) bit group, . . . , the 87^(th) bit group to the178^(th) bit group, and the 112^(th) bit group to the 179^(th) bitgroup.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 55 presented below.

TABLE 55 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 57 154 144 171 111 5 38 82 15 122 99 54 26 151 136110 67 41 4 87 164 178 16 Group-wise 77 150 123 140 97 53 112 42 63 16523 78 7 125 176 138 89 153 40 116 65 28 163 interleaver 52 106 2 131 83147 12 177 95 32 167 44 59 114 73 84 139 149 124 13 27 101 0 input, 61113 174 91 74 50 157 134 20 35 1 64 102 169 118 75 46 158 128 141 36 318 100 86 56 172 71 160 119 145 43 29 11 96 107 133 173 85 68 159 143 4937 24 117 6 130 179 80 66 104 142 166 48 17 33 92 120 132 79 156 62 109175 51 14 39 90 121 137 25 72 161 103 148 58 10 47 93 127 115 22 34 70162 152 60 8 105 45 129 81 94 30 19 170 146 69 9 55 108 135 125 98 31 8821 168 155 76

In the case of Table 55, Equation 21 may be expressed asY₀=X_(π(0))=X₅₇, Y₁=X_(π(1))=X₁₅₄, Y₂=X_(π(2))=X₁₄₄, . . . ,Y₁₇₈=X_(π(178))=X₁₅₅, and Y₁₇₉=X_(π(179))=X₇₆. Accordingly, the groupinterleaver 122 may rearrange the order of the plurality of bit groupsin bit group wise by changing the 57^(th) bit group to the 0^(th) bitgroup, the 154^(th) bit group to the 1^(st) bit group, the 144^(th) bitgroup to the 2^(nd) bit group, . . . , the 155^(th) bit group to the178^(th) bit group, and the 76^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is64800, the code rate is 6/15, and the modulation method is QPSK, π(j)may be defined as in Table 56 presented below.

TABLE 56 Order of bits group to be block interleaved π(j) (0 ≤ j < 180)j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 4243 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6263 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8485 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 π(j)-th block of 127 38 14 83 58 72 107 150 0 179 117 138 161 22 4482 32 100 56 5 69 120 133 Group-wise 168 17 157 147 87 104 39 4 60 29121 131 15 172 156 73 142 43 95 106 59 119 85 interleaver 21 7 153 17770 37 130 141 54 103 167 155 24 88 154 75 35 10 128 143 52 178 64 input,112 89 166 99 34 13 76 155 134 48 65 114 23 145 2 98 124 12 86 159 46176 62 108 148 25 1 136 74 96 36 158 118 169 47 11 146 57 132 79 67 9430 111 170 160 3 144 49 125 19 84 61 101 113 171 71 9 31 135 45 149 9120 55 110 163 81 123 6 33 174 137 66 18 94 50 109 77 152 126 162 40 8 28173 93 140 63 78 151 122 51 41 105 27 165 90 175 139 80 68 16 129 116 5342 26 164 102 92

In the case of Table 56, Equation 21 may be expressed asY₀=X_(π(0))=X₁₂₇, Y₁=X_(π(1))=X₃₈, Y₂X_(π(2))=X₁₄, Y₁₇₈X_(π(178))=X₁₀₂,and Y₁₇₉=X_(π(179))=X₉₂. Accordingly, the group interleaver 122 mayrearrange the order of the plurality of bit groups in bit group wise bychanging the 127^(th) bit group to the 0^(th) bit group, the 38^(th) bitgroup to the 1^(st) bit group, the 14^(th) bit group to the 2^(nd) bitgroup, . . . , the 102^(nd) bit group to the 178^(th) bit group, and the92^(nd) bit group to the 179^(th) bit group.

As described above, the group interleaver 122 may rearrange the order ofthe plurality of bit groups in bit group wise by using Equation 21 andTables 32 to 56.

“j-th block of Group-wise Interleaver output” in Tables 32 to 56indicates the j-th bit group output from the group interleaver 122 afterinterleaving, and “π(j)-th block of Group-wise Interleaver input”indicates the π(j)-th bit group input to the group interleaver 122.

In addition, since the order of the bit groups constituting the LDPCcodeword is rearranged by the group interleaver 122 in bit group wise,and then the bit groups are block-interleaved by the block interleaver124, which will be described below, “Order of bits groups to be blockinterleaved” is set forth in Tables 32 to 56 in relation to π(j).

The LDPC codeword which is group-interleaved in the above-describedmethod is illustrated in FIG. 7 . Comparing the LDPC codeword of FIG. 7and the LDPC codeword of FIG. 6 before group interleaving, it can beseen that the order of the plurality of bit groups constituting whereinQ_(ldpc) is a cyclic shift parameter value regarding columns in a columngroup of an information word submatrix of the parity check matrix,N_(ldpc) is a length of the LDPC codeword, and K_(ldp), is a length ofinformation word bits of the LDPC codeword.

the LDPC codeword is rearranged.

That is, as shown in FIGS. 6 and 7 , the groups of the LDPC codeword arearranged in order of bit group X₀, bit group X₁, . . . , bit groupX_(Ngroup-1) before being group-interleaved, and are arranged in anorder of bit group Y₀, bit group Y₁, . . . , bit group Y_(Ngroup-1)after being group-interleaved. In this case, the order of arranging thebit groups by the group interleaving may be determined based on Tables32 to 56.

The group twist interleaver 123 interleaves bits in a same group. Thatis, the group twist interleaver 123 may rearrange the order of the bitsin the same bit group by changing the order of the bits in the same bitgroup.

In this case, the group twist interleaver 123 may rearrange the order ofthe bits in the same bit group by cyclic-shifting a predetermined numberof bits from among the bits in the same bit group.

For example, as shown in FIG. 8 , the group twist interleaver 123 maycyclic-shift bits included in the bit group Y₁ to the right by 1 bit. Inthis case, the bits located in the 0^(th) position, the 1^(st) position,the 2^(nd) position, . . . , the 358^(th) position, and the 359^(th)position in the bit group Y₁ as shown in FIG. 8 are cyclic-shifted tothe right by 1 bit. As a result, the bit located in the 359^(th)position before being cyclic-shifted is located in the front of the bitgroup Y₁ and the bits located in the 0^(th) position, the 1^(st)position, the 2^(nd) position, . . . , the 358^(th) position beforebeing cyclic-shifted are shifted to the right serially by 1 bit andlocated.

In addition, the group twist interleaver 123 may rearrange the order ofbits in each bit group by cyclic-shifting a different number of bits ineach bit group.

For example, the group twist interleaver 123 may cyclic-shift the bitsincluded in the bit group Y₁ to the right by 1 bit, and may cyclic-shiftthe bits included in the bit group Y₂ to the right by 3 bits.

However, the above-described group twist interleaver 123 may be omittedaccording to circumstances.

In addition, the group twist interleaver 123 is placed after the groupinterleaver 122 in the above-described example. However, this is merelyan example. That is, the group twist interleaver 123 changes only theorder of bits in a certain bit group and does not change the order ofthe bit groups. Therefore, the group twist interleaver 123 may be placedbefore the group interleaver 122.

The block interleaver 124 interleaves the plurality of bit groups theorder of which has been rearranged. Specifically, the block interleaver124 may interleave the plurality of bit groups the order of which hasbeen rearranged by the group interleaver 122 in bit group wise (or bitgroup unit). The block interleaver 124 is formed of a plurality ofcolumns each including a plurality of rows and may interleave bydividing the plurality of rearranged bit groups based on a modulationorder determined according to a modulation method.

In this case, the block interleaver 124 may interleave the plurality ofbit groups the order of which has been rearranged by the groupinterleaver 122 in bit group wise. Specifically, the block interleaver124 may interleave by dividing the plurality of rearranged bit groupsaccording to a modulation order by using a first part and a second part.

Specifically, the block interleaver 124 interleaves by dividing each ofthe plurality of columns into a first part and a second part, writingthe plurality of bit groups in the plurality of columns of the firstpart serially in bit group wise, dividing the bits of the other bitgroups into groups (or sub bit groups) each including a predeterminednumber of bits based on the number of columns, and writing the sub bitgroups in the plurality of columns of the second part serially.

Herein, the number of bit groups which are interleaved in bit group wisemay be determined by at least one of the number of rows and columnsconstituting the block interleaver 124, the number of bit groups and thenumber of bits included in each bit group. In other words, the blockinterleaver 124 may determine the bit groups which are to be interleavedin bit group wise considering at least one of the number of rows andcolumns constituting the block interleaver 124, the number of bit groupsand the number of bits included in each bit group, interleave thecorresponding bit groups in bit group wise, and divide bits of the otherbit groups into sub bit groups and interleave the sub bit groups. Forexample, the block interleaver 124 may interleave at least part of theplurality of bit groups in bit group wise using the first part, anddivide bits of the other bit groups into sub bit groups and interleavethe sub bit groups using the second part.

Meanwhile, interleaving bit groups in bit group wise means that the bitsincluded in the same bit group are written in the same column. In otherwords, the block interleaver 124, in case of bit groups which areinterleaved in bit group wise, may not divide the bits included in thesame bit groups and write the bits in the same column, and in case ofbit groups which are not interleaved in bit group wise, may divide thebits in the bit groups and write the bits in different columns.

Accordingly, the number of rows constituting the first part is amultiple of the number of bits included in one bit group (for example,360), and the number of rows constituting the second part may be lessthan the number of bits included in one bit group.

In addition, in all bit groups interleaved by the first part, the bitsincluded in the same bit group are written and interleaved in the samecolumn of the first part, and in at least one group interleaved by thesecond part, the bits are divided and written in at least two columns ofthe second part.

The specific interleaving method will be described later.

Meanwhile, the group twist interleaver 123 changes only the order ofbits in the bit group and does not change the order of bit groups byinterleaving. Accordingly, the order of the bit groups to beblock-interleaved by the block interleaver 124, that is, the order ofthe bit groups to be input to the block interleaver 124, may bedetermined by the group interleaver 122. Specifically, the order of thebit groups to be block-interleaved by the block interleaver 124 may bedetermined by π(j) defined in Tables 32 to 56.

As described above, the block interleaver 124 may interleave theplurality of bit groups the order of which has been rearranged in bitgroup wise by using the plurality of columns each including theplurality of rows.

In this case, the block interleaver 124 may interleave the LDPC codewordby dividing the plurality of columns into at least two parts. Forexample, the block interleaver 124 may divide each of the plurality ofcolumns into the first part and the second part and interleave theplurality of bit groups constituting the LDPC codeword.

In this case, the block interleaver 124 may divide each of the pluralityof columns into N number of parts (N is an integer greater than or equalto 2) according to whether the number of bit groups constituting theLDPC codeword is an integer multiple of the number of columnsconstituting the block interleaver 124, and may perform interleaving.

When the number of bit groups constituting the LDPC codeword is aninteger multiple of the number of columns constituting the blockinterleaver 124, the block interleaver 124 may interleave the pluralityof bit groups constituting the LDPC codeword in bit group wise withoutdividing each of the plurality of columns into parts.

Specifically, the block interleaver 124 may interleave by writing theplurality of bit groups of the LDPC codeword on each of the columns inbit group wise in a column direction, and reading each row of theplurality of columns in which the plurality of bit groups are written inbit group wise in a row direction.

In this case, the block interleaver 124 may interleave by writing bitsincluded in a predetermined number of bit groups which corresponds to aquotient obtained by dividing the number of bit groups of the LDPCcodeword by the number of columns of the block interleaver 124 on eachof the plurality of columns serially in a column direction, and readingeach row of the plurality of columns in which the bits are written in arow direction.

Hereinafter, the group located in the j^(th) position after beinginterleaved by the group interleaver 122 will be referred to as groupY_(j).

For example, it is assumed that the block interleaver 124 is formed of Cnumber of columns each including R₁ number of rows. In addition, it isassumed that the LDPC codeword is formed of N_(group) number of bitgroups and the number of bit groups N_(group) is a multiple of C.

In this case, when the quotient obtained by dividing N_(group) number ofbit groups constituting the LDPC codeword by C number of columnsconstituting the block interleaver 124 is A (=N_(group)/C) (A is aninteger greater than 0), the block interleaver 124 may interleave bywriting A (=N_(group)/C) number of bit groups on each column serially ina column direction and reading bits written on each column in a rowdirection.

For example, as shown in FIG. 9 , the block interleaver 124 writes bitsincluded in bit group Y₀, bit group Y₁, . . . bit group Y_(A−1) in the1^(st) column from the 1^(st) row to the R₁ ^(th) row, writes bitsincluded in bit group Y_(A), bit group Y_(A+1), . . . , bit groupY_(2A−1) in the 2nd column from the 1^(st) row to the R₁ ^(th) row, . .. , and writes bits included in bit group Y_(CA−A), bit groupY_(CA−A+1), . . . , bit group Y_(CA−1) in the column C from the 1^(st)row to the R₁ ^(th) row. The block interleaver 124 may read the bitswritten in each row of the plurality of columns in a row direction.

Accordingly, the block interleaver 124 interleaves all bit groupsconstituting the LDPC codeword in bit group wise.

However, when the number of bit groups of the LDPC codeword is not aninteger multiple of the number of columns of the block interleaver 124,the block interleaver 124 may divide each column into 2 parts andinterleave a part of the plurality of bit groups of the LDPC codeword inbit group wise, and divide bits of the other bit groups into sub bitgroups and interleave the sub bit groups. In this case, the bitsincluded in the other bit groups, that is, the bits included in thenumber of groups which correspond to the remainder when the number ofbit groups constituting the LDPC codeword is divided by the number ofcolumns are not interleaved in bit group wise, but interleaved by beingdivided according to the number of columns.

Specifically, the block interleaver 124 may interleave the LDPC codewordby dividing each of the plurality of columns into two parts.

In this case, the block interleaver 124 may divide the plurality ofcolumns into the first part and the second part based on at least one ofthe number of columns of the block interleaver 124, the number of bitgroups of the LDPC codeword, and the number of bits of bit groups.

Here, each of the plurality of bit groups may be formed of 360 bits. Inaddition, the number of bit groups of the LDPC codeword is determinedbased on the length of the LDPC codeword and the number of bits includedin the bit group. For example, when an LDPC codeword in the length of16200 is divided such that each bit group has 360 bits, the LDPCcodeword is divided into 45 bit groups. Alternatively, when an LDPCcodeword in the length of 64800 is divided such that each bit group has360 bits, the LDPC codeword may be divided into 180 bit groups. Further,the number of columns constituting the block interleaver 124 may bedetermined according to a modulation method. This will be explained indetail below.

Accordingly, the number of rows constituting each of the first part andthe second part may be determined based on the number of columnsconstituting the block interleaver 124, the number of bit groupsconstituting the LDPC codeword, and the number of bits constituting eachof the plurality of bit groups.

Specifically, in each of the plurality of columns, the first part may beformed of as many rows as the number of bits included in at least onebit group which can be written in each column in bit group wise fromamong the plurality of bit groups of the LDPC codeword, according to thenumber of columns constituting the block interleaver 124, the number ofbit groups constituting the LDPC codeword, and the number of bitsconstituting each bit group.

In each of the plurality of columns, the second part may be formed ofrows excluding as many rows as the number of bits included in at leastsome bit groups which can be written in each of the plurality of columnsin bit group wise. Specifically, the number rows of the second part maybe the same value as a quotient when the number of bits included in allbit groups excluding bit groups corresponding to the first part isdivided by the number of columns constituting the block interleaver 124.In other words, the number of rows of the second part may be the samevalue as a quotient when the number of bits included in the remainingbit groups which are not written in the first part from among bit groupsconstituting the LDPC codeword is divided by the number of columns.

That is, the block interleaver 124 may divide each of the plurality ofcolumns into the first part including as many rows as the number of bitsincluded in bit groups which can be written in each column in bit groupwise, and the second part including the other rows.

Accordingly, the first part may be formed of as many rows as the numberof bits included in bit groups, that is, as many rows as an integermultiple of M. However, since the number of codeword bits constitutingeach bit group may be an aliquot part of M as described above, the firstpart may be formed of as many rows as an integer multiple of the numberof bits constituting each bit group.

In this case, the block interleaver 124 may interleave by writing andreading the LDPC codeword in the first part and the second part in thesame method.

Specifically, the block interleaver 124 may interleave by writing theLDPC codeword in the plurality of columns constituting each of the firstpart and the second part in a column direction, and reading theplurality of columns constituting the first part and the second part inwhich the LDPC codeword is written in a row direction.

That is, the block interleaver 124 may interleave by writing the bitsincluded in at least some bit groups which can be written in each of theplurality of columns in bit group wise in each of the plurality ofcolumns of the first part serially, dividing the bits included in theother bit groups except the at least some bit groups and writing in eachof the plurality of columns of the second part in a column direction,and reading the bits written in each of the plurality of columnsconstituting each of the first part and the second part in a rowdirection.

In this case, the block interleaver 124 may interleave by dividing theother bit groups except the at least some bit groups from among theplurality of bit groups based on the number of columns constituting theblock interleaver 124.

Specifically, the block interleaver 124 may interleave by dividing thebits included in the other bit groups by the number of a plurality ofcolumns, writing each of the divided bits in each of a plurality ofcolumns constituting the second part in a column direction, and readingthe plurality of columns constituting the second part, where the dividedbits are written, in a row direction.

That is, the block interleaver 124 may divide the bits included in theother bit groups except the bit groups written in the first part fromamong the plurality of bit groups of the LDPC codeword, that is, thebits in the number of bit groups which correspond to the remainder whenthe number of bit groups constituting the LDPC codeword is divided bythe number of columns, by the number of columns, and may write thedivided bits in each column of the second part serially in a columndirection.

For example, it is assumed that the block interleaver 124 is formed of Cnumber of columns each including R₁ number of rows. In addition, it isassumed that the LDPC codeword is formed of N_(group) number of bitgroups, the number of bit groups N_(group) is not a multiple of C, andA×C+1=N_(group) (A is an integer greater than 0). In other words, it isassumed that when the number of bit groups constituting the LDPCcodeword is divided by the number of columns, the quotient is A and theremainder is 1.

In this case, as shown in FIGS. 10 and 11 , the block interleaver 124may divide each column into a first part including R₁ number of rows anda second part including R₂ number of rows. In this case, R₁ maycorrespond to the number of bits included in bit groups which can bewritten in each column in bit group wise, and R₂ may be R₁ subtractedfrom the number of rows of each column.

That is, in the above-described example, the number of bit groups whichcan be written in each column in bit group wise is A, and the first partof each column may be formed of as many rows as the number of bitsincluded in A number of bit groups, that is, may be formed of as manyrows as A×M number.

In this case, the block interleaver 124 writes the bits included in thebit groups which can be written in each column in bit group wise, thatis, A number of bit groups, in the first part of each column in thecolumn direction.

That is, as shown in FIGS. 10 and 11 , the block interleaver 124 writesthe bits included in each of bit group Y₀, bit group Y₁, . . . , groupY_(A−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 1^(st)column, writes bits included in each of bit group Y_(A), bit groupY_(A+1), . . . , bit group Y_(2A−1) in the 1^(st) to R₁ ^(th) rows ofthe first part of the 2^(nd) column, . . . , writes bits included ineach of bit group Y_(CA−A), bit group Y_(CA−A+1), . . . , bit groupY_(CA−1) in the 1^(st) to R₁ ^(th) rows of the first part of the columnC.

As described above, the block interleaver 124 writes the bits includedin the bit groups which can be written in each column in bit group wisein the first part of each column.

In other words, in the above exemplary embodiment, the bits included ineach of bit group (Y₀), bit group (Y₁), . . . , bit group (Y_(A−1)) maynot be divided and all of the bits may be written in the first column,the bits included in each of bit group (Y_(A)), bit group (Y_(A+1)), . .. , bit group (Y_(2A−1)) may not be divided and all of the bits may bewritten in the second column, and the bits included in each of bit group(Y_(CA−A)), bit group (Y_(CA−A+1)), . . . , group (Y_(CA−1)) may not bedivided and all of the bits may be written in the C column. As such, allbit groups interleaved by the first part are written in the same columnof the first part.

Thereafter, the block interleaver 124 divides bits included in the othergroups except the bit groups written in the first part of each columnfrom among the plurality of bit groups, and writes the bits in thesecond part of each column in the column direction. In this case, theblock interleaver 124 divides the bits included in the other bit groupsexcept the bit groups written in the first part of each column by thenumber of columns, so that the same number of bits are written in thesecond part of each column, and writes the divided bits in the secondpart of each column in the column direction.

In the above-described example, since A×C+1=N_(group) when the bitgroups constituting the LDPC codeword are written in the first partserially, the last bit group Y_(Ngroup−1) of the LDPC codeword is notwritten in the first part and remains. Accordingly, the blockinterleaver 124 divides the bits included in the bit group Y_(Ngroup−1)into C number of sub bit groups as shown in FIG. 10 , and writes thedivided bits (that is, the bits corresponding to the quotient when thebits included in the last group (Y_(Ngroup−1)) are divided by C) in thesecond part of each column serially.

The bits divided based on the number of columns may be referred to assub bit groups. In this case, each of the sub bit groups may be writtenin each column of the second part. That is, the bits included in the bitgroups may be divided and may form the sub bit groups.

That is, the block interleaver 124 writes the bits in the 1^(st) to R₂^(th) rows of the second part of the 1^(st) column, writes the bits inthe 1^(st) to R₂ ^(th) rows of the second part of the 2^(nd) column, . .. , and writes the bits in the 1^(st) to R₂ ^(th) rows of the secondpart of the column C. In this case, the block interleaver 124 may writethe bits in the second part of each column in the column direction asshown in FIG. 10 .

That is, in the second part, the bits constituting the bit group may notbe written in the same column and may be written in the plurality ofcolumns. In other words, in the above example, the last bit group(Y_(Ngroup−1)) is formed of M number of bits and thus, the bits includedin the last bit group (Y_(Ngroup−1)) may be divided by M/C and writtenin each column. That is, the bits included in the last bit group(Y_(Ngroup−1)) are divided by M/C, forming M/C number of sub bit groups,and each of the sub bit groups may be written in each column of thesecond part.

Accordingly, in at least one bit group which is interleaved by thesecond part, the bits included in the at least one bit group are dividedand written in at least two columns constituting the second part.

In the above-described example, the block interleaver 124 writes thebits in the second part in the column direction. However, this is merelyan example. That is, the block interleaver 124 may write the bits in theplurality of columns of the second parts in a row direction. In thiscase, the block interleaver 124 may write the bits in the first part inthe same method as described above.

Specifically, referring to FIG. 11 , the block interleaver 124 writesthe bits from the 1^(st) row of the second part in the 1^(st) column tothe 1^(st) row of the second part in the column C, writes the bits fromthe 2^(nd) row of the second part in the 1^(st) column to the 2^(nd) rowof the second part in the column C, . . . , etc., and writes the bitsfrom the R₂ ^(th) row of the second part in the 1st column to the R₂^(th) row of the second part in the column C.

On the other hand, the block interleaver 124 reads the bits written ineach row of each part serially in the row direction. That is, as shownin FIGS. 10 and 11 , the block interleaver 124 reads the bits written ineach row of the first part of the plurality of columns serially in therow direction, and reads the bits written in each row of the second partof the plurality of columns serially in the row direction.

Accordingly, the block interleaver 124 may interleave a part of theplurality of bit groups constituting the LDPC codeword in bit groupwise, and divide and interleave some of the remaining bit groups. Thatis, the block interleaver 124 may interleave by writing the LDPCcodeword constituting a predetermined number of bit groups from amongthe plurality of bit groups in the plurality of columns of the firstpart in bit group wise, dividing the bits of the other bit groups andwriting the bits in each of the columns of the second part, and readingthe plurality of columns of the first and second parts in the rowdirection.

As described above, the block interleaver 124 may interleave theplurality of bit groups in the methods described above with reference toFIGS. 9 to 11 .

In particular, in the case of FIG. 10 , the bits included in the bitgroup which does not belong to the first part are written in the secondpart in the column direction and read in the row direction. In view ofthis, the order of the bits included in the bit group which does notbelong to the first part is rearranged. Since the bits included in thebit group which does not belong to the first part are interleaved asdescribed above, Bit Error Rate (BER)/Frame Error Rate (FER) performancecan be improved in comparison with a case in which such bits are notinterleaved.

However, the bit group which does not belong to the first part may notbe interleaved as shown in FIG. 11 . That is, since the blockinterleaver 124 writes and read the bits included in the group whichdoes not belong to the first part in and from the second part in the rowdirection, the order of the bits included in the group which does notbelong to the first part is not changed and the bits are output to themodulator 130 serially. In this case, the bits included in the groupwhich does not belong to the first part may be output serially andmapped onto a modulation symbol.

In FIGS. 10 and 11 , the last single bit group of the plurality of bitgroups is written in the second part. However, this is merely anexample. The number of bit groups written in the second part may varyaccording to the total number of bit groups of the LDPC codeword, thenumber of columns and rows, the number of transmission antennas, etc.

The block interleaver 124 may have a configuration as shown in Tables 57and 58 presented below:

TABLE 57 N_(ldpc) = 64800 QPSK 16 QAM 64 QAM 256 QAM 1024 QAM 4096 QAM C2 4 6 8 10 12 R₁ 32400 16200 10800 7920 6480 5400 R₂ 0 0 0 180 0 0

TABLE 58 N_(ldpc) = 16200 QPSK 16 QAM 64 QAM 256 QAM 1024 QAM 4096 QAM C2 4 6 8 10 12 R₁ 7920 3960 2520 1800 1440 1080 R₂ 180 90 180 225 180 270

Herein, C (or N_(C)) is the number of columns of the block interleaver124, R₁ is the number of rows constituting the first part in eachcolumn, and R₂ is the number of rows constituting the second part ineach column.

Referring to Tables 57 and 58, the number of columns has the same valueas a modulation order according to a modulation method, and each of aplurality of columns is formed of rows corresponding to the number ofbits constituting the LDPC codeword divided by the number of a pluralityof columns.

For example, when the length N_(ldpc) of the LDPC codeword is 64800 andthe modulation method is QPSK, the block interleaver 124 is formed of 2columns as the modulation order is 2 in the case of QPSK, and eachcolumn is formed of rows as many as R₁+R₂=32400(=64800/2).

Meanwhile, referring to Tables 57 and 58, when the number of bit groupsconstituting an LDPC codeword is an integer multiple of the number ofcolumns, the block interleaver 124 interleaves without dividing eachcolumn. Therefore, R₁ corresponds to the number of rows constitutingeach column, and R₂ is 0. In addition, when the number of bit groupsconstituting an LDPC codeword is not an integer multiple of the numberof columns, the block interleaver 124 interleaves the groups by dividingeach column into the first part formed of R₁ number of rows, and thesecond part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is equal to thenumber of bits constituting a modulation symbol, bits included in a samebit group are mapped onto a single bit of each modulation symbol asshown in Tables 57 and 58.

For example, when N_(ldpc)=64800 and the modulation method is QPSK, theblock interleaver 124 may be formed of two (2) columns each including32400 rows. In this case, a plurality of bit groups are written in thetwo (2) columns in bit group wise and bits written in the same row ineach column are output serially. In this case, since two (2) bitsconstitute a single modulation symbol in the modulation method of QPSK,bits included in the same bit group, that is, bits output from a singlecolumn, may be mapped onto a single bit of each modulation symbol. Forexample, bits included in a bit group written in the 1^(st) column maybe mapped onto the first bit of each modulation symbol.

Referring to Tables 57 and 58, the total number of rows of the blockinterleaver 124, that is, R₁+R₂, is N_(ldpc)/C.

In addition, the number of rows of the first part, R₁, is an integermultiple of the number of bits included in each group, M (e.g., M=360),and may be expressed as └N_(group)/C┘×M, and the number of rows of thesecond part, R₂, may be N_(ldpc)/C−R₁. Herein, └N_(group)/C┘ is thelargest integer below N_(group)/C. Since R₁ is an integer multiple ofthe number of bits included in each group, M, bits may be written in R₁in bit groups wise.

In addition, when the number of bit groups of the LDPC codeword is not amultiple of the number of columns, it can be seen from Tables 57 and 58that the block interleaver 124 interleaves by dividing each column intotwo parts.

Specifically, the length of the LDPC codeword divided by the number ofcolumns is the total number of rows included in the each column. In thiscase, when the number of bit groups of the LDPC codeword is a multipleof the number of columns, each column is not divided into two parts.However, when the number of bit groups of the LDPC codeword is not amultiple of the number of columns, each column is divided into twoparts.

For example, it is assumed that the number of columns of the blockinterleaver 124 is identical to the number of bits constituting amodulation symbol, and an LDPC codeword is formed of 64800 bits as shownin Table 57. In this case, each bit group of the LDPC codeword is formedof 360 bits, and the LDPC codeword is formed of 64800/360 (=180) bitgroups.

When the modulation method is QPSK, the block interleaver 124 may beformed of two (2) columns and each column may have 64800/2 (=32400)rows.

In this case, since the number of bit groups of the LDPC codeworddivided by the number of columns is 180/2 (=90), bits can be written ineach column in bit group wise without dividing each column into twoparts. That is, bits included in 90 bit groups which is the quotientwhen the number of bit groups constituting the LDPC codeword is dividedby the number of columns, that is, 90×360 (=32400) bits can be writtenin each column.

However, when the modulation method is 256-QAM, the block interleaver124 may be formed of eight (8) columns and each column may have64800/8(=8100) rows.

In this case, since the number of bit groups of the LDPC codeworddivided by the number of columns is 180/8=22.5, the number of bit groupsconstituting the LDPC codeword is not an integer multiple of the numberof columns. Accordingly, the block interleaver 124 divides each of theeight (8) columns into two parts to perform interleaving in bit groupwise.

In this case, since the bits should be written in the first part of eachcolumn in bit group wise, the number of bit groups which can be writtenin the first part of each column in bit group wise is 22 which is thequotient when the number of bit groups constituting the LDPC codeword isdivided by the number of columns, and accordingly, the first part ofeach column has 22×360 (=7920) rows. Accordingly, 7920 bits included in22 bit groups may be written in the first part of each column.

The second part of each column has rows which are the rows of the firstpart subtracted from the total rows of each column. Accordingly, thesecond part of each column includes 8100−7920 (=180) rows.

In this case, the bits included in the other bit groups which have notbeen written in the first part are divided and written in the secondpart of each column.

Specifically, since 22×8 (=176) bit groups are written in the firstpart, the number of bit groups to be written in the second part is180−176 (=4) (for example, bit group Y₁₇₆, bit group Y₁₇₇, bit groupY₁₇₈, and bit group Y₁₇₉ from among bit group Y₀, bit group Y₁, bitgroup Y₂, . . . , bit group Y₁₇₈, and bit group Y₁₇₉ constituting theLDPC codeword).

Accordingly, the block interleaver 124 may write the four (4) bit groupswhich have not been written in the first part and remains from among thegroups constituting the LDPC codeword in the second part of each columnserially.

That is, the block interleaver 124 may write 180 bits of the 360 bitsincluded in the bit group Y₁₇₆ in the 1^(st) row to the 180^(th) row ofthe second part of the 1^(st) column in the column direction, and maywrite the other 180 bits in the 1^(st) row to the 180^(th) row of thesecond part of the 2^(nd) column in the column direction. In addition,the block interleaver 124 may write 180 bits of the 360 bits included inthe bit group Y₁₇₇ in the 1^(st) row to the 180^(th) row of the secondpart of the 3^(rd) column in the column direction, and may write theother 180 bits in the 1^(st) row to the 180^(th) row of the second partof the 4^(th) column in the column direction. In addition, the blockinterleaver 124 may write 180 bits of the 360 bits included in the bitgroup Y₁₇₈ in the 1^(st) row to the 180^(th) row of the second part ofthe 5^(th) column in the column direction, and may write the other 180bits in the 1^(st) row to the 180^(th) row of the second part of the6^(th) column in the column direction. In addition, the blockinterleaver 124 may write 180 bits of the 360 bits included in the bitgroup Y₁₇₉ in the 1^(st) row to the 180^(th) row of the second part ofthe 7^(th) column in the column direction, and may write the other 180bits in the 1^(st) row to the 180^(th) row of the second part of the8^(th) column in the column direction.

Accordingly, the bits included in the bit group which has not beenwritten in the first part and remains are not written in the same columnin the second part and may be divided and written in the plurality ofcolumns.

Hereinafter, the block interleaver of FIG. 5 according to an exemplaryembodiment will be explained in detail with reference to FIG. 12 .

In a group-interleaved LDPC codeword (v₀, v₁, . . . , v_(N) _(ldpc) ⁻¹),Y_(j) is continuously arranged like V={Y₀, Y₁, . . . Y_(N) _(group) ⁻¹}.

The LDPC codeword after group interleaving may be interleaved by theblock interleaver 124 as shown in FIG. 12 . In this case, the blockinterleaver 124 divide a plurality of columns into the first part(Part 1) and the second part (Part 2) based on the number of columns ofthe block interleaver 124 and the number of bits of bit groups. In thiscase, in the first part, the bits constituting the bit groups may bewritten in the same column, and in the second part, the bitsconstituting the bit groups may be written in a plurality of columns(i.e. the bits constituting the bit groups may be written in at leasttwo columns).

Specifically, input bits v_(i) are written serially from the first partto the second part column wise, and then read out serially from thefirst part to the second part row wise. That is, the data bits v_(i) arewritten serially into the block interleaver column-wise starting in thefirst part and continuing column-wise finishing in the second part, andthen read out serially row-wise from the first part and then row-wisefrom the second part. Accordingly, the bit included in the same bitgroup in the first part may be mapped onto a single bit of eachmodulation symbol.

In this case, the number of columns and the number of rows of the firstpart and the second part of the block interleaver 124 vary according toa modulation format and a length of the LDPC codeword as in Table 30presented below. That is, the first part and the second part blockinterleaving configurations for each modulation format and code lengthare specified in Table 59 presented below. Herein, the number of columnsof the block interleaver 124 may be equal to the number of bitsconstituting a modulation symbol. In addition, a sum of the number ofrows of the first part, N_(r1) and the number of rows of the secondpart, N_(r2), is equal to N_(ldpc)/N_(C) (herein, N_(C) is the number ofcolumns). In addition, since N_(r1)(=└N_(group)/N_(c)┘×360) is amultiple of 360, a multiple of bit groups may be written in the firstpart.

TABLE 59 Rows in Part 1 N_(r1) Rows in Part 2 N_(r2) Columns ModulationN_(ldpc) = 64800 N_(ldpc) = 16200 N_(ldpc) = 64800 N_(ldpc) = 16200N_(c) QPSK 32400 7920  0 180  2  16-QAM 16200 3960  0  90  4  64-QAM10800 2520  0 180  6  256-QAM  7920 1800 180 225  8 1024-QAM  6480 1440 0 180 10 4096-QAM  5400 1080  0 270 12

Hereinafter, an operation of the block interleaver 124 will be explainedin detail.

Specifically, as shown in FIG. 12 , the input bit v_(i)(0≤i<N_(C)×N_(r1)) is written in r_(i) row of c_(i) column of the firstpart of the block interleaver 124. Herein, c_(i) and r_(i) are

$c_{i} = \left\lfloor \frac{i}{N_{r1}} \right\rfloor$and r_(i)=(i mod N_(r1)), respectively.

In addition, the input bit v_(i) (N_(C)×N_(r1)≤i<N_(ldpc)) is written inan r_(i) row of c_(i) column of the second part of the block interleaver124. Herein, c_(i) and r_(i) satisfy

$c_{i} = \left\lfloor \frac{\left( {i - {N_{C} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor$and r_(i)=N_(r1)+{(i−N_(C)×N_(r1)) mod N_(r2)}, respectively.

An output bit q_(j)(0≤j<N_(ldpc)) is read from c_(j) column of r_(j)row. Herein, r_(j) and c_(j) satisfy

$r_{j} = \left\lfloor \frac{j}{N_{c}} \right\rfloor$and c_(j)=(j mod N_(C)), respectively.

For example, when the length N_(ldpc) of an LDPC codeword is 64800 andthe modulation method is 256-QAM, the order of bits output from theblock interleaver 124 may be (q₀, q₁, q₂, . . . , q₆₃₃₅₇, q₆₃₃₅₈,q₆₃₃₅₉, q₆₃₃₆₀, q₆₃₃₆₁, . . . , q₆₄₇₉₉)=(v₀, v₇₉₂₀, v₁₅₈₄₀, . . . ,v₄₇₅₁₉, v₅₅₄₃₉, v₆₃₃₅₉, v₆₃₃₆₀, v₆₃₅₄₀, . . . , v₆₄₇₉₉). Herein, theindexes of the right side of the foregoing equation may be specificallyexpressed for the eight (8) columns as 0, 7920, 15840, 23760, 31680,39600, 47520, 55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441,. . . , 7919, 15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360,63540, 63720, 63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719,63899, 64079, 64259, 64439, 64619, 64799.

Hereinafter, the interleaving operation of the block interleaver 124will be explained in detail.

The block interleaver 124 may interleave by writing a plurality of bitgroups in each column in bit group wise in a column direction, andreading each row of the plurality of columns in which the plurality ofbit groups are written in bit group wise in a row direction.

In this case, the number of columns constituting the block interleaver124 may vary according to a modulation method, and the number of rowsmay be the length of the LDPC codeword/the number of columns. Forexample, when the modulation method is QPSK, the block interleaver 124may be formed of 2 columns. In this case, when the length N_(ldpc), ofthe LDPC codeword is 16200, the number of rows is 8100 (=16200/2), and,when the length N_(ldpc) of the LDPC codeword is 64800, the number ofrows is 32400 (=64800/2).

Hereinafter, the method for interleaving the plurality of bit groups inbit group wise by the block interleaver 124 will be explained in detail.

When the number of bit groups constituting the LDPC codeword is aninteger multiple of the number of columns, the block interleaver 124 mayinterleave by writing the bit groups as many as the number of bit groupsdivided by the number of columns in each column serially in bit groupwise.

For example, when the modulation method is QPSK and the length N_(ldpc)of the LDPC codeword is 64800, the block interleaver 124 may be formedof two (2) columns each including 32400 rows. In this case, since theLDPC codeword is divided into (64800/360=180) number of bit groups whenthe length N_(ldpc), of the LDPC codeword is 64800, the number of bitgroups (=180) of the LDPC codeword may be an integer multiple of thenumber of columns (=2) when the modulation method is QPSK.

In this case, as shown in FIG. 13 , the block interleaver 124 writes thebits included in each of the bit group Y₀, bit group Y₁, . . . , bitgroup Y₈₉ in the 1^(st) row to 32400^(th) row of the first column, andwrites the bits included in each of the bit group Y₉₀, the bit groupY₉₁, . . . , the bit group Y₁₇₉ in the 1^(st) row to 32400^(th) row ofthe second column. In addition, the block interleaver 124 may read thebits written in each row of the two columns serially in the rowdirection.

However, when the number of bit groups constituting the LDPC codeword isnot an integer multiple of the number of columns, the block interleaver124 may interleave by dividing each column into N number of parts (N isan integer greater than or equal to 2).

Specifically, the block interleaver 124 may divide each column into apart including as many rows as the number of bits included in the bitgroup which can be written in each column in bit group wise, and a partincluding the other rows, and may interleave by using the divided parts.

In this case, the block interleaver 124 may write at least some bitgroups which can be written in each of the plurality of columns in bitgroup wise from among the plurality of bit groups in each of theplurality of columns serially, and then divides the bits included in theother bit groups into sub bit groups and writes the bits in the otherarea remaining in each of the plurality of columns after the at leastsome bit groups are written in bit group wise. That is, the blockinterleaver 124 may write the bits included in at least some bit groupswhich are writable in the first part of each column in bit group wise,and may divide the bits included in the other bit groups and writhe thebits in the second part of each column.

For example, when the modulation method is QPSK and the length N_(ldpc)of the LDPC codeword is 16200, the block interleaver 124 may be formedof two (2) columns each including 8100 rows. In this case, since theLDPC codeword is divided into (16200/360=45) number of bit groups whenthe length N_(ldpc), of the LDPC codeword is 16200, the number of bitgroups (=45) of the LDPC codeword is not an integer multiple of thenumber of columns (=2) when the modulation method is QPSK. That is, aremainder exists.

In this case, the block interleaver 124 may divide each column into thefirst part including 7920 rows and the second part including 180 rows asshown in FIGS. 14 and 15 .

The block interleaver 124 writes the bits included in the bit groupswhich can be written in each column in bit group wise in the first partof each column in the column direction.

That is, as shown in FIGS. 14 and 15 , the block interleaver 124 writesthe bits included in each of the bit group Y₀, bit group Y₁, . . . , bitgroup Y₂₁ in the 1^(st) row to 7920^(th) row of the first part of thefirst column, and writes the bits included in each of the bit group Y₂₂,the bit group Y₂₃, . . . , the bit group Y₄₃ in the 1^(st) row to7920^(th) row of the first part of the second column.

As described above, the block interleaver 124 writes the bits includedin the bit groups which can be written in each column in bit group wisein the first part of each column in bit group wise.

Thereafter, the block interleaver 124 divides the bits included in theother bit groups except for the bit groups written in the first part ofeach column from among the plurality of bit groups, and writes the bitsin the second part of each column in the column direction. In this case,the block interleaver 124 may divide the bits included in the other bitgroups except for the bit groups written in the first part of eachcolumn by the number of columns, such that the same number of bits arewritten in the second part of each column, and writes the divided bitsin each column of the second part in the column direction.

For example, when the bit group Y₄₄, which is the last bit group of theLDPC codeword, remains as shown in FIG. 14 , the block interleaver 124divides the bits included in the bit group Y₄₄ by 2, and writes thedivided bits in the second part of each column serially.

That is, the block interleaver 124 may write the bits in the 1^(st) rowto 180^(th) row of the second part of the first column, and writes thebits in the 1^(st) row to 180^(th) row of the second part of the secondcolumn. In this case, the block interleaver 124 may write the bits inthe second part of each column in the column direction as shown in FIG.14 . That is, the bits constituting the bit group are not written in thesame column in the second part and are written in the plurality ofcolumns.

In the above-described example, the block interleaver 124 writes thebits in the second part in the column direction. However, this is merelyan example. That is, the block interleaver 124 may write the bits in theplurality of columns of the second part in the row direction. However,the block interleaver 124 may write the bits in the first part in thesame method as described above.

Specifically, referring to FIG. 15 , the block interleaver 124 may writethe bits in the 1^(st) row of the second part of the first column to the1^(st) row of the second part of the second column, writes the bits inthe 2^(nd) row of the second part of the first column to the 2^(nd) rowof the second part of the second column, . . . , writes the bits in the180^(th) row of the second part of the first column to the 180^(th) rowof the second part of the second column.

The block interleaver 124 reads the bits written in each row of eachpart serially in the row direction. That is, as shown in FIGS. 14 and 15, the block interleaver 124 may read the bits written in each row of thefirst part of the plurality of columns serially in the row direction,and may read the bits written in each row of the second part of theplurality of columns serially in the row direction.

As described above, the block interleaver 124 may interleave theplurality of bit groups in the method described above with reference toFIGS. 13 to 15 .

The modulator 130 maps the interleaved LDPC codeword onto a modulationsymbol. Specifically, the modulator 130 may demultiplex the interleavedLDPC codeword, modulate the demultiplexed LDPC codeword, and map theLDPC codeword onto a constellation.

In this case, the modulator 130 may generate a modulation symbol usingthe bits included in each of a plurality of bit groups.

In other words, as described above, the bits included in different bitgroups are written in each column of the block interleaver 124, and theblock interleaver 124 reads the bits written in each column in the rowdirection. In this case, the modulator 130 generates a modulation symbolby mapping the bits read in each column onto each bit of the modulationsymbol. Accordingly, each bit of the modulation symbol belongs to adifferent group.

For example, it is assumed that the modulation symbol consists of Cnumber of bits. In this case, the bits which are read from each row of Cnumber of columns of the block interleaver 124 may be mapped onto eachbit of the modulation symbol and thus, each bit of the modulation symbolconsisting of C number of bits belong to C number of different groups.

Hereinbelow, the above feature will be described in greater detail.

First, the modulator 130 demultiplexes the interleaved LDPC codeword. Toachieve this, the modulator 130 may include a demultiplexer (not shown)to demultiplex the interleaved LDPC codeword.

The demultiplexer (not shown) demultiplexes the interleaved LDPCcodeword. Specifically, the demultiplexer (not shown) performsserial-to-parallel conversion with respect to the interleaved LDPCcodeword, and demultiplexes the interleaved LDPC codeword into a cellhaving a predetermined number of bits (or a data cell).

For example, as shown in FIG. 16 , the demultiplexer (not shown)receives an LDPC codeword Q=(q₀, q₁, q₂, . . . ) output from theinterleaver 120, outputs the received LDPC codeword bits to a pluralityof substreams serially, converts the input LDPC codeword bits intocells, and outputs the cells.

In this case, bits having a same index in each of the plurality ofsubstreams may constitute a same cell. Accordingly, the cells may beconfigured like (y_(0,0), y_(1,0), y_(ηMOD−1,0))=(q₀, q₁, q_(ηMOD−1)),(y_(0,1), y_(1,1), . . . , y_(ηMOD−1,1))=(q_(ηMOD), q_(ηMOD+1), . . . ,q_(2xηMOD−1)), . . . .

Herein, the number of substreams, N_(substreams), may be equal to thenumber of bits constituting a modulation symbol, η_(MOD). Accordingly,the number of bits constituting each cell may be equal to the number ofbits constituting a modulation symbol (that is, a modulation order).

For example, when the modulation method is QPSK, the number of bitsconstituting the modulation symbol, η_(MOD), is 2, and thus, the numberof substreams, N_(substreams), is 2, and the cells may be configuredlike (y_(0,0), y_(1,0))=(q₀, q₁), (y_(0,1), y_(1,1))(q₂, q₃), (y_(0,2),y_(1,2))(q₄, q₅), . . . .

The modulator 130 may map the demultiplexed LDPC codeword ontomodulation symbols.

Specifically, the modulator 130 may modulate bits (that is, cells)output from the demultiplexer (not shown) in various modulation methods.For example, when the modulation method is QPSK, 16-QAM, 64-QAM,256-QAM, 1024-QAM, and 4096-QAM, the number of bits constituting amodulation symbol, η_(MOD) (that is, the modulation order), may be 2, 4,6, 8, 10 and 12, respectively.

In this case, since each cell output from the demultiplexer (not shown)is formed of as many bits as the number of bits constituting amodulation symbol, the modulator 130 may generate a modulation symbol bymapping each cell output from the demultiplexer (not shown) onto aconstellation point serially. Herein, a modulation symbol corresponds toa constellation point on a constellation.

However, the above-described demultiplexer (not shown) may be omittedaccording to circumstances. In this case, the modulator 130 may generatemodulation symbols by grouping a predetermined number of bits frominterleaved bits serially and mapping the predetermined number of bitsonto constellation points. In this case, the modulator 130 may generatemodulation symbols by mapping η_(MOD) number of bits onto theconstellation points serially according to a modulation method.

When an LDPC codeword is generated based on the parity check matrixdefined as in Tables 4 to 21 and Tables 23 to 31, a plurality of bitgroups of the LDPC codeword are interleaved by using interleavingparameters defined as in Tables 32 to 56 for the following reasons.

In general, when modulation is performed by using QPSK,encoding/decoding performance depends on how LDPC codeword bits aremapped onto two bits of a QPSK symbol.

In particular, when two parity bits are connected to a single check nodein a parity check matrix, good performance can be guaranteed by mappingthe two parity bits onto a single QPSK symbol. In addition, goodperformance can be guaranteed by mapping two parity bits connected to asingle check node in the parity check matrix onto a single QPSK symbol.In addition, when there are a plurality of parity bits each connected toa single check node in a parity check matrix, good performance can beguaranteed by selecting two check nodes and mapping two parity bitsconnected to the two check nodes onto a single QPSK symbol.

Accordingly, after the LDPC codeword bits generated based on the paritycheck matrix defined as in Tables 4 to 21 and Tables 23 to 31 aregroup-interleaved based on Equation 21 and Tables 32 to 56, when theinterleaved LDPC codeword bits are modulated by QPSK, two parity bitsconnected to a single check node may be mapped onto a same QPSK symbolor two parity bits connected to the selected two check nodes may bemapped onto a same QPSK symbol. Accordingly, encoding/decodingperformance can be improved and the transmitting apparatus is robust toa burst error.

Specifically, since the order of bit groups to be written/read in theplurality of columns of the block interleaver 124 is determinedaccording to the interleaving in bit group wise in the group interleaver122, bits to be mapped onto a modulation symbol may be determinedaccording to the interleaving in bit group wise in the group interleaver122.

Accordingly, the group interleaver 122 may interleave the LDPC codewordbits in bit group wise such that bits belonging to a predeterminednumber of continuous bit groups, that is, bits connected to apredetermined number of same check nodes, are mapped onto a same QPSKsymbol, by considering reliability of bits mapped onto a modulationsymbol and performance of the codeword bits of the LDPC codeword. Toachieve this, the group interleaver 122 may interleave the LDPC codewordbits in bit group wise based on Equation 21 and Tables 32 to 56.

Hereinafter, a method for designing the group interleaver 122 accordingto an exemplary embodiment will be explained. For the convenience ofexplanation, a method for defining π(j) with reference to Table 33 fromamong Tables 32 to 56 by way of an example will be explained.

In the case of the QPSK modulation method, the block interleaver 124 isformed of two columns, and two bits read and output from a same row oftwo columns configure a same QPSK symbol. Accordingly, bits ofcontinuous bit groups from among the plurality of bit groups of the LDPCcodeword should be written in a same row in each of the two columns ofthe block interleaver 124 to be mapped onto a same QPSK symbol.

That is, in order to map two parity bits connected to a single checknode in the parity check matrix onto a same QPSK modulation symbol, bitsbelonging to two continuous bit groups to which the two parity bitsbelong should be written in a same row in each of the two columns of theblock interleaver 124.

When bits included in two continuous bit groups from the 25^(th) bitgroup to the 44^(th) bit group from among 45 bit groups constituting anLDPC codeword (that is, the 0^(th) to 44^(th) bit groups) should bemapped onto a same QPSK symbol for the purpose of improvingencoding/decoding performance, and it is assumed that the 26^(th) bitgroup, 28^(th) bit group, . . . , 42^(nd) bit group, and 44^(th) bitgroups are written in the 4321^(st) row to the 7920^(th) row of thefirst part of the first column of the block interleaver 124 as shown in(a) of FIG. 17 , the 25^(th) bit group, 27^(th) bit group, . . . ,41^(st) bit group, and 43^(rd) bit group should be written in the4321^(st) row to the 7920^(th) row of the first part of the secondcolumn.

In this case, encoding/decoding performance depends on which bit groupsare mapped onto a same modulation symbol (in the above-describedexample, two continuous bit groups from the 25^(th) bit group to the44^(th) bit group are mapped onto the same modulation symbol).Therefore, the other bit groups may be randomly written in the blockinterleaver 124.

That is, in the above-described example, the 0^(th) bit group to the24^(th) bit group may be randomly written in the other rows of the firstpart and the second part which remain after the 25^(th) bit group to the44^(th) bit group are written in the block interleaver 124. For example,as shown in (a) of FIG. 17 , the 3^(rd) bit group, 22^(nd) bit group,7^(th) bit group, . . . , 2^(nd) bit group, 23^(rd) bit group, 11^(th)bit group, 0^(th) bit group, 13^(th) bit group, . . . , 12^(th) bitgroup, and 16^(th) bit group may be written in the other rows of thefirst part, and the 8^(th) bit group may be written in the second part.

However, when the LDPC codeword bits are written in each column of theblock interleaver 124 in bit group wise as shown in (a) of FIG. 17 , thebits included in the 25^(th) bit group to the 44^(th) bit group aremapped onto continuous QPSK symbols, and thus, are vulnerable to a busterror.

Accordingly, in order not to map the bits included in the 25^(th) bitgroup to the 44^(th) bit group onto continuous QPSK symbols, the rows ofthe block interleaver 124 may be randomly interleaved (row-wise randominterleaving) as shown in (a) of FIG. 17 and the order of the bit groupsto be written in the block interleaver 124 may be changed as shown in(b) of FIG. 17 .

As a result, when the group interleaver 122 interleaves a plurality ofbit groups of an LDPC codeword in the order shown in Table 33, theplurality of bit groups of the LDPC codeword may be written in the blockinterleaver 124 in the order shown in (b) of FIG. 17 , and accordingly,parity bits included in two continuous bit groups may be mapped onto asame QPSK symbol.

That is, when the encoder 110 performs LDPC-encoding in a code rate of7/15 based on a parity check matrix including an information wordsubmatrix defined by the Table 6 and a parity submatrix having a dualdiagonal configuration, and the plurality of bit groups of the LDPCcodeword are interleaved by the group interleaver 122 based on π(j)defined by Table 33, the plurality of bit groups of the LDPC codewordmay be written in the block interleaver 124 as shown in (b) of FIG. 17 ,and thus, bits included in two continuous bit groups of 20 bit groupsmay be mapped onto a same modulation symbol.

In (a) and (b) of FIG. 17 , bits included in two continuous bit groupsof the 20 bit groups from the 25^(th) bit group to the 44^(th) bit groupare mapped onto a same modulation symbol. However, this is merely anexample. The number of continuous bit groups to be mapped onto a samemodulation symbol may vary according to a parity check matrix and a coderate. That is, when LDPC encoding is performed with a parity checkmatrix having a different configuration and at a different code rate,the number of continuous bit groups to be mapped onto a same modulationsymbol may be changed.

Hereinafter, a method for defining π(j) with reference to Table 36according to another exemplary embodiment will be explained.

In the case of the QPSK modulation method, the block interleaver 124 isformed of two columns, and two bits read and output from a same row oftwo columns configure a same QPSK symbol. Accordingly, bits ofcontinuous bit groups from among a plurality of bit groups of an LDPCcodeword should be written in a same row in each of two columns of theblock interleaver 124 to be mapped onto a same QPSK symbol.

That is, in order to map two parity bits connected to a single checknode in a parity check matrix onto a same QPSK modulation symbol, bitsbelonging to two continuous bit groups to which the two parity bitsbelong should be written in a same row in each of two columns of theblock interleaver 124.

When bits included in two continuous bit groups from the 39^(th) bitgroup to the 44^(th) bit group from among 45 bit groups constituting anLDPC codeword (that is, the 0^(th) to 44^(th) bit groups) should bemapped onto a same QPSK symbol for the purpose of improvingencoding/decoding performance, and it is assumed that the 40^(th) bitgroup, 42^(nd) bit group, and 44^(th) bit groups are written in the 6840row to the 7920^(th) row of the first part of the first column of theblock interleaver 124 as shown in (a) of FIG. 18 , the 39^(th) bitgroup, 41^(st) bit group, and 43^(rd) bit group should be written in the6840^(st) row to the 7920^(th) row of the first part of the secondcolumn.

In this case, encoding/decoding performance depends on which bit groupsare mapped onto a same modulation symbol (in the above-describedexample, two continuous bit groups from the 39^(th) bit group to the44^(th) bit group are mapped onto a same modulation symbol). Therefore,the other bit groups may be randomly written in the block interleaver124.

That is, in the above-described example, the 0^(th) bit group to the38^(th) bit group may be randomly written in the other rows of the firstpart and the second part which remain after the 39^(th) bit group to the44^(th) bit group are written in the block interleaver 124. For example,as shown in (a) of FIG. 18 , the 13^(th) bit group, 10^(th) bit group,0^(th) bit group, . . . , 36^(th) bit group, 38^(th) bit group, 6^(th)bit group, 7^(th) bit group, 17^(th) bit group, . . . , bit group, and37^(th) bit group may be written in the other rows of the first part,and the 1^(st) bit group may be written in the second part.

However, when LDPC codeword bits are written in each column of the blockinterleaver 124 in bit group wise as shown in (a) of FIG. 18 , bitsincluded in the 39^(th) bit group to the 44^(th) bit group are mappedonto continuous QPSK symbols, and thus, are vulnerable to a bust error.

Accordingly, in order not to map bits included in the 39^(th) bit groupto the 44^(th) bit group onto continuous QPSK symbols, the rows of theblock interleaver 124 may be randomly interleaved (row-wise randominterleaving) as shown in (a) of FIG. 18 and the order of the bit groupsto be written in the block interleaver 124 may be changed as shown in(b) of FIG. 18 .

As a result, when the group interleaver 122 interleaves a plurality ofbit groups of an LDPC codeword in the order shown in Table 36, theplurality of bit groups of the LDPC codeword may be written in the blockinterleaver 124 in the order shown in (b) of FIG. 18 , and accordingly,parity bits included in two continuous bit groups may be mapped onto asame QPSK symbol.

That is, when the encoder 110 performs LDPC-encoding in a code rate of13/15 based on a parity check matrix including an information wordsubmatrix defined by Table 12 and a parity submatrix having a dualdiagonal configuration, and the plurality of bit groups of the LDPCcodeword are interleaved by the group interleaver 122 based on π(j)defined by Table 36, the plurality of bit groups of the LDPC codewordmay be written in the block interleaver 124 as shown in (b) of FIG. 18 ,and thus, bits included in two continuous bit groups of 6 bit groups maybe mapped onto a same modulation symbol.

In (a) and (b) of FIG. 18 , bits included in two continuous bit groupsof the 6 bit groups from the 39^(th) bit group to the 44^(th) bit groupare mapped onto a same modulation symbol. However, this is merely anexample. The number of continuous bit groups to be mapped onto a samemodulation symbol may vary according to a parity check matrix and a coderate. That is, when LDPC encoding is performed with a parity checkmatrix having a different configuration and at a different code rate,the number of continuous bit groups to be mapped onto a same modulationsymbol may be changed.

In addition, since performance is greatly affected by which continuousbit groups are mapped onto a same modulation symbol, the other bitgroups except for the continuous bit groups mapped onto the samemodulation symbol may be randomly written in the plurality of columns asshown in (a) and (b) of FIG. 17 or (a) and (b) of FIG. 18 .

Accordingly, as long as a same bit group is mapped onto a samemodulation symbol, interleaving may be regarded as being performed inthe same method as the group interleaver presented in the presentdisclosure.

TABLE 60 A A_perm B_perm C_perm D_perm E_perm (j)-th (j)-th (j)-th(j)-th (j)-th (j)-th j-th block block of block of block of block ofblock of block of of Groupwise Groupwise Groupwise Groupwise GroupwiseGroupwise Groupwise Interleaver Interleaver Interleaver InterleaverInterleaver Interleaver Interleaver output input input input input inputinput 0 3 4 0 2 17 23 1 22 22 2 1 16 22 2 7 23 19 3 18 24 3 18 44 44 4444 44 4 6 34 34 34 34 34 5 1 1 10 17 0 9 6 4 3 11 15 3 7 7 14 2 9 16 2 58 5 32 32 32 32 32 9 15 42 42 42 42 42 10 2 6 20 6 12 18 11 23 15 23 711 19 12 26 30 30 30 30 30 13 28 40 40 40 40 40 14 30 18 16 10 21 3 1532 5 15 11 22 1 16 34 28 28 28 28 28 17 36 38 38 38 38 38 18 38 7 6 21 814 19 40 14 5 22 7 13 20 42 26 26 26 26 26 21 44 36 36 36 36 36 22 11 913 18 5 8 23 0 0 14 24 23 10 24 13 16 12 19 4 6 25 10 43 43 43 43 43 2621 33 33 33 33 33 27 17 17 1 0 1 16 28 9 11 4 20 6 15 29 19 12 3 5 24 1730 24 31 31 31 31 31 31 20 41 41 41 41 41 32 12 21 18 4 19 4 33 16 20 179 20 2 34 25 29 29 29 29 29 35 27 39 39 39 39 39 36 29 10 8 8 10 0 37 3124 7 23 9 21 38 33 27 27 27 27 27 39 35 37 37 37 37 37 40 37 13 24 12 1420 41 39 19 22 13 15 12 42 41 25 25 25 25 25 43 43 35 35 35 35 35 44 8 821 14 13 11

For example, in Table 60, A and A_perm indicate π(j) after/beforerow-wise random interleaving is performed, and B_perm, C_perm, D_perm,and E_perm indicate π(j) when row-wise random interleaving is performedafter the other bit groups except for continuous bit groups are randomlywritten in the plurality of columns in different methods. Referring toTable 60, in B_perm, C_perm, D_perm, and E_perm, the same group as inA_perm is mapped onto a same modulation symbol. Accordingly, it can beseen that a same interleaving method as in A_perm is used for B_perm,C_perm, D_perm, and E_perm.

In the above-described example, an interleaving pattern in the case of aparity check matrix having the configuration of FIG. 2 has beendescribed. Hereinafter, a method for designing an interleaving patternwhen a parity check matrix has the configuration of FIG. 4 will beexplained with reference to Table 32.

When there are bit groups formed of parity bits connected to a singlecheck node from among a plurality of bit groups of the LDPC codeword,bits included in two bit groups selected from the corresponding bitgroups should be written in a same row of two columns of the blockinterleaver 124.

It is assumed that the 18^(th) bit group to the 44^(th) bit group fromamong the 45 bit groups (that is, 0^(th) to 44^(th) bit groups) of anLDPC codeword are bit groups formed of parity bits connected to a singlecheck node connected to a single parity bit, and two bits are selectedfrom the corresponding bit groups and 2880 (=8×360) QPSK symbols intotal should be generated.

In this case, as shown in (a) of FIG. 19 , 8 bit groups randomlyselected from among the 18^(th) bit group to the 44^(th) bit groupshould be written in the 5041^(st) row to the 7920^(th) row of the firstpart of the first column, and the other 8 bit groups randomly selectedshould be written in the 5041^(st) row to the 7920^(th) row of the firstpart of the second column.

Since encoding/decoding performance depends on how many QPSK symbols areformed of parity bits connected to a single check node connected to asingle parity bit, the other bit groups may be randomly written in theblock interleaver 124.

Accordingly, the 29 bit groups which are not selected in theabove-described example may be randomly written in the other rows of thefirst part, and the second part which remain after the selected groupsare written in the block interleaver 124. For example, as shown in (a)of FIG. 19 , the 0^(th) bit group, 17^(th) bit group, 38^(th) bit group,. . . , 37^(th) bit group, 5^(th) bit group, and 3^(rd) bit group may bewritten in the other rows of the first part, and the 8^(th) bit groupmay be written in the second part.

However, when LDPC codeword bits are written in each column of the blockinterleaver 124 in bit group wise as shown in (a) of FIG. 19 , a busterror may be intensively generated only in the parity bit, and thus, mayundermine encoding/decoding performance of the LDPC code. Accordingly,the rows of the block interleaver 124 may be randomly interleaved asshown in (a) of FIG. 19 , and the order of the bit groups to be writtenin the block interleaver 124 may be changed as shown in (b) of FIG. 19 ,so that a bust error does not affect only the parity bit if any.

As a result, when the group interleaver 122 interleaves a plurality ofbit groups of an LDPC codeword in the order of Table 32, the pluralityof bit groups of the LDPC codeword may be written in the blockinterleaver 124 in the order shown in (b) of FIG. 19 , and accordingly,a QPSK symbol formed of only parity bits connected to a check nodeconnected to a single parity bit may be generated.

That is, when the encoder 110 performs LDPC encoding based on the paritycheck matrix defined in Table 26 at a code rate of 5/15, and the groupinterleaver 122 interleaves a plurality of bit groups of an LDPCcodeword based on π(j) defined by Table 32, the plurality of bit groupsof the LDPC codeword may be written in the block interleaver 124 asshown in (b) of FIG. 19 , and thus, bits included in two continuous bitgroups of 16 bit groups may be mapped onto a same modulation symbol.

In (a) and (b) of FIG. 19 , only the 16 bit groups are randomly selectedfrom the 18^(th) bit group to the 44^(th) bit group and a modulationsymbol formed of only bits included in selected bit groups is generated.However, this is merely an example. The number of bit groups,corresponding to parity bits connected to a check node connected to asingle parity bit, which are mapped onto a same modulation symbol, maybe changed according to a parity check matrix and a code rate.

The transmitting apparatus 100 may transmit a modulation symbol to areceiving apparatus 1300. For example, the modulator 130 may map themodulation symbol onto an Orthogonal Frequency Division Multiplexing(OFDM) frame using OFDM, and may transmit the modulation symbol mappedonto the OFDM frame to the receiving apparatus 1300 through an allocatedchannel.

FIG. 20 is a block diagram to illustrate a configuration of a receivingapparatus according to an exemplary embodiment. Referring to FIG. 20 ,the receiving apparatus 1500 includes a demodulator 1510, a multiplexer1520, a deinterleaver 1530 and a decoder 1540.

The demodulator 1510 receives and demodulates a signal transmitted fromthe transmitting apparatus 100. Specifically, the demodulator 1510generates a value corresponding to an LDPC codeword by demodulating thereceived signal, and outputs the value to the multiplexer 1520. In thiscase, the demodulator 1510 may use a demodulation method correspondingto a modulation method used in the transmitting apparatus 100. To do so,the transmitting apparatus 100 may transmit information regarding themodulation method to the receiving apparatus 1500, or the transmittingapparatus 100 may perform modulation using a pre-defined modulationmethod between the transmitting apparatus 100 and the receivingapparatus 1500.

The value corresponding to the LDPC codeword may be expressed as achannel value for the received signal. There are various methods fordetermining the channel value, and for example, a method for determininga Log Likelihood Ratio (LLR) value may be the method for determining thechannel value.

The LLR value is a log value for a ratio of the probability that a bittransmitted from the transmitting apparatus 100 is 0 and the probabilitythat the bit is 1. In addition, the LLR value may be a bit value whichis determined by a hard decision, or may be a representative value whichis determined according to a section to which the probability that thebit transmitted from the transmitting apparatus 100 is 0 or 1 belongs.

The multiplexer 1520 multiplexes the output value of the demodulator1510 and outputs the value to the deinterleaver 1530.

Specifically, the multiplexer 1520 is an element corresponding to ademultiplexer (not shown) provided in the transmitting apparatus 100,and performs an operation corresponding to the demultiplexer (notshown). That is, the multiplexer 1520 performs an inverse operation ofthe operation of the demultiplexer (not shown), and performs cell-to-bitconversion with respect to the output value of the demodulator 1510 andoutputs the LLR value in the unit of bit. However, when thedemultiplexer (not shown) is omitted from the transmitting apparatus100, the multiplexer 1520 may be omitted from the receiving apparatus1500.

The information regarding whether the demultiplexing operation isperformed or not may be provided by the transmitting apparatus 100, ormay be pre-defined between the transmitting apparatus 100 and thereceiving apparatus 1500.

The deinterleaver 1530 deinterleaves the output value of the multiplexer1520 and outputs the values to the decoder 1540.

Specifically, the deinterleaver 1530 is an element corresponding to theinterleaver 120 of the transmitting apparatus 100 and performs anoperation corresponding to the interleaver 120. That is, thedeinterleaver 1530 deinterleaves the LLR value by performing theinterleaving operation of the interleaver 120 inversely.

To do so, the deinterleaver 1530 may include a block deinterleaver 1531,a group twist deinterleaver 1532, a group deinterleaver 1533, and aparity deinterleaver 1534 as shown in FIG. 21 .

The block deinterleaver 1531 deinterleaves the output of the multiplexer1520 and outputs a value to the group twist deinterleaver 1532.

Specifically, the block deinterleaver 1531 is an element correspondingto the block interleaver 124 provided in the transmitting apparatus 100and performs the interleaving operation of the block interleaver 124inversely.

That is, the block deinterleaver 1531 deinterleaves by writing the LLRvalue output from the multiplexer 1520 in each row in the row directionand reading each column of the plurality of rows in which the LLR valueis written in the column direction by using at least one row formed ofthe plurality of columns.

In this case, when the block interleaver 124 interleaves by dividing thecolumn into two parts, the block deinterleaver 1531 may deinterleave bydividing the row into two parts.

In addition, when the block interleaver 124 writes and reads in and fromthe group that does not belong to the first part in the row direction,the block deinterleaver 1531 may deinterleave by writing and readingvalues corresponding to the group that does not belong to the first partin the row direction.

Hereinafter, the block deinterleaver 1531 will be explained withreference to FIG. 22 . However, this is merely an example and the blockdeinterleaver 1531 may be implemented in other methods.

An input LLR v_(i) (0≤i<N_(ldpc)) is written in a r_(i) row and a c_(i)column of the block deinterleaver 1531. Herein, c_(i)=(i mod N_(c)) and

${r_{i} = \left\lfloor \frac{i}{N_{c}} \right\rfloor},$

On the other hand, an output LLR q_(i)(0≤i<N_(c)×N_(r1)) is read from ac_(i) column and a r_(i) row of the first part of the blockdeinterleaver 1531. Herein,

${c_{i} = \left\lfloor \frac{i}{N_{r1}} \right\rfloor},$r_(i)=(i mod N_(r1)).

In addition, an output LLR q_(i)(N_(c)×N_(r1)≤i<N_(ldpc)) is read from ac_(i) column and a r_(i) row of the second part. Herein,

${c_{i} = \left\lfloor \frac{\left( {i - {N_{C} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor},$r_(i)=N_(r1)+{(i−N_(c)×N_(r1)) mode N_(r2)}.

The group twist deinterleaver 1532 deinterleaves the output value of theblock deinterleaver 1531 and outputs the value to the groupdeinterleaver 1533.

Specifically, the group twist deinterleaver 1532 is an elementcorresponding to the group twist interleaver 123 provided in thetransmitting apparatus 100, and may perform the interleaving operationof the group twist interleaver 123 inversely.

That is, the group twist deinterleaver 1532 may rearrange the LLR valuesof the same bit group by changing the order of the LLR values existingin the same bit group. When the group twist operation is not performedin the transmitting apparatus 100, the group twist deinterleaver 1532may be omitted.

The group deinterleaver 1533 (or the group-wise deinterleaver)deinterleaves an output value of the group twist deinterleaver 1532 andoutputs a value to the parity deinterleaver 1534.

Specifically, the group deinterleaver 1533 is an element correspondingto the group interleaver 122 provided in the transmitting apparatus 100and may perform the interleaving operation of the group interleaver 122inversely.

That is, the group deinterleaver 1533 may rearrange the order of theplurality of bit groups in bit group wise. In this case, the groupdeinterleaver 1533 may rearrange the order of the plurality of bitgroups in bit group wise by applying the interleaving method of Tables32 to 56 inversely according to a length of the LDPC codeword, amodulation method and a code rate.

The parity deinterleaver 1534 performs parity deinterleaving withrespect to an output value of the group deinterleaver 1533 and outputs avalue to the decoder 1540.

Specifically, the parity deinterleaver 1534 is an element correspondingto the parity interleaver 121 provided in the transmitting apparatus 100and may perform the interleaving operation of the parity interleaver 121inversely. That is, the parity deinterleaver 1534 may deinterleave theLLR values corresponding to the parity bits from among the LLR valuesoutput from the group deinterleaver 1533. In this case, the paritydeinterleaver 1534 may deinterleave the LLR value corresponding to theparity bits inversely to the parity interleaving method of Equation 8.

However, the parity deinterleaver 1534 may be omitted depending on thedecoding method and embodiment of the decoder 1540.

Although the deinterleaver 1530 of FIG. 20 includes three (3) or four(4) elements as shown in FIG. 21 , operations of the elements may beperformed by a single element. For example, when bits each of whichbelongs to each of bit groups X_(a) and X_(b) constitute a singlemodulation symbol, the deinterleaver 1530 may deinterleave these bits tolocations corresponding to their bit groups based on the received singlemodulation symbol.

For example, when the code rate is 13/15 and the modulation method isQPSK, the group deinterleaver 1533 may perform deinterleaving based onTable 36.

In this case, bits each of which belongs to each of bit groups Y₃(=X₃₈)and Y₂₅(=X₃₇) may constitute a single modulation symbol. Since one bitin each of the bit groups Y₃(=X₃₈) and Y₂₅(=X₃₇) constitutes a singlemodulation symbol, the deinterleaver 1530 may map bits onto decodinginitial values corresponding to the bit groups Y₃(=X₃₈) and Y₂₅(=X₃₇)based on the received single modulation symbol.

The decoder 1540 may perform LDPC decoding by using the output value ofthe deinterleaver 1530. To achieve this, the decoder 1540 may include anLDPC decoder (not shown) to perform the LDPC decoding.

Specifically, the decoder 1540 is an element corresponding to theencoder 110 of the transmitting apparatus 100 and may correct an errorby performing the LDPC decoding by using the LLR value output from thedeinterleaver 1530.

For example, the decoder 1540 may perform the LDPC decoding in aniterative decoding method based on a sum-product algorithm. Thesum-product algorithm is one example of a message passing algorithm, andthe message passing algorithm refers to an algorithm which exchangesmessages (e.g., LLR value) through an edge on a bipartite graph,calculates an output message from messages input to variable nodes orcheck nodes, and updates.

The decoder 1540 may use a parity check matrix when performing the LDPCdecoding. In this case, the parity check matrix used in the decoding mayhave the same configuration as that of the parity check matrix used inthe encoding of the encoder 110, and this has been described above withreference to FIGS. 2 to 4 .

In addition, information on the parity check matrix and information onthe code rate, etc. which are used in the LDPC decoding may bepre-stored in the receiving apparatus 1500 or may be provided by thetransmitting apparatus 100.

FIG. 23 is a flowchart to illustrate an interleaving method of atransmitting apparatus according to an exemplary embodiment.

First, an LDPC codeword is generated by LDPC encoding based on a paritycheck matrix (S1710).

Thereafter, the LDPC codeword is interleaved (S1720). In this case, theLDPC codeword may be interleaved such that bits included in continuousbit groups from among a plurality of bit groups of the LDPC codeword aremapped onto a same modulation symbol. In addition, when there are aplurality of check nodes connected only to a single parity bit in theparity check matrix of the LDPC codeword, the LDPC codeword may beinterleaved such that bits included in bit groups corresponding to theparity bit connected to the corresponding check nodes are selectivelymapped onto a same modulation symbol.

Then, the interleaved LDPC codeword is mapped onto a modulation symbol(S1730). That is, the bits included in the continuous bit groups fromamong the plurality of bit groups of the LDPC codeword may be mappedonto a same modulation symbol. In addition, when there are a pluralityof check nodes connected only to a single parity bit in the parity checkmatrix of the LDPC codeword, the bits included in bit groupscorresponding to the parity bit connected to the corresponding checknodes may be selectively mapped onto a same modulation symbol.

Each of the plurality of bit groups may be formed of M number of bits,and M may be a common divisor of N_(ldpc), and K_(ldpc) and may bedetermined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Herein, Q_(ldpc)is a cyclic shift parameter value regarding columns in a column group ofan information word submatrix of the parity check matrix, N_(ldpc) is alength of the LDPC codeword, and K_(ldpc) is a length of informationword bits of the LDPC codeword.

Operation S1720 may include parity-interleaving parity bits of the LDPCcodeword, dividing the parity-interleaved LDPC codeword by the pluralityof bit groups and rearranging an order of the plurality of bit groups inbit group wise, and interleaving the plurality of bit groups the orderof which is rearranged.

The order of the plurality of bit groups may be rearranged in bit groupwise based on the above-described Equation 21 presented above.

In Equation 21, π(j) is determined based on at least one of a length ofthe LDPC codeword and a code rate.

For example, when the LDPC codeword has a length of 16200, themodulation method is QPSK, and the code rate is 13/15, π(j) in Equation21 may be defined as in Table 36 presented above.

Operation S1720 may include dividing the LDPC codeword by the pluralityof bit groups and rearranging an order of the plurality of bit groups inbit group wise, and interleaving the plurality of bit groups the orderof which is rearranged.

The order of the plurality of bit groups may be rearranged in bit groupwise based on Equation 21 presented above.

π(j) in Equation 21 may be determined based on at least one of a lengthof the LDPC codeword and a code rate.

For example, when the LDPC codeword has a length of 16200, themodulation method is QPSK, and the code rate is 5/15, π(j) in Equation21 may be defined as in Table 32 presented above.

However, this is merely an example. The order of the plurality of bitgroups may be rearranged in bit group wise by using one of Tables 32 to56 and Equation 21.

The interleaving the plurality of bit groups may include: writing theplurality of bit groups in each of a plurality of columns in bit groupwise in a column direction, and reading each row of the plurality ofcolumns in which the plurality of bit groups are written in bit groupwise in a row direction.

In addition, the interleaving the plurality of bit groups may include:serially write, in the plurality of columns, at least some bit groupwhich is writable in the plurality of columns in bit group wise fromamong the plurality of bit groups, and then dividing and writing theother bit groups in an area which remains after the at least some bitgroup is written in the plurality of columns in bit group wise.

A non-transitory computer readable medium, which stores a program forperforming the interleaving methods according to various exemplaryembodiments in sequence, may be provided.

The non-transitory computer readable medium refers to a medium thatstores data semi-permanently rather than storing data for a very shorttime, such as a register, a cache, and a memory, and is readable by anapparatus. Specifically, the above-described various applications orprograms may be stored in a non-transitory computer readable medium suchas a compact disc (CD), a digital versatile disk (DVD), a hard disk, aBlu-ray disk, a universal serial bus (USB), a memory card, and a readonly memory (ROM), and may be provided.

At least one of the components, elements or units represented by a blockas illustrated in FIGS. 1, 5, 16, 20 and 21 may be embodied as variousnumbers of hardware, software and/or firmware structures that executerespective functions described above, according to an exemplaryembodiment. For example, at least one of these components, elements orunits may use a direct circuit structure, such as a memory, processing,logic, a look-up table, etc. that may execute the respective functionsthrough controls of one or more microprocessors or other controlapparatuses. Also, at least one of these components, elements or unitsmay be specifically embodied by a module, a program, or a part of code,which contains one or more executable instructions for performingspecified logic functions. Also, at least one of these components,elements or units may further include a processor such as a centralprocessing unit (CPU) that performs the respective functions, amicroprocessor, or the like. Further, although a bus is not illustratedin the above block diagrams, communication between the components,elements or units may be performed through the bus. Functional aspectsof the above exemplary embodiments may be implemented in algorithms thatexecute on one or more processors. Furthermore, the components, elementsor units represented by a block or processing steps may employ anynumber of related art techniques for electronics configuration, signalprocessing and/or control, data processing and the like.

The foregoing exemplary embodiments and advantages are merely exemplaryand are not to be construed as limiting the present inventive concept.The exemplary embodiments can be readily applied to other types ofapparatuses. Also, the description of the exemplary embodiments isintended to be illustrative, and not to limit the scope of the inventiveconcept, and many alternatives, modifications, and variations will beapparent to those skilled in the art.

What is claimed is:
 1. A broadcast signal receiving apparatuscomprising: a receiver configured to receive a broadcast signal from abroadcast signal transmitting apparatus; a demodulator configured todemodulate the broadcast signal to generate values based on quadraturephase shift keying (QPSK) modulation; a deinterleaver configured todeinterleave the values, split the deinterleaved values into a pluralityof groups, and deinterleave the plurality of groups; and a decoderconfigured to decode values of the deinterleaved plurality of groupsbased on a low density parity check (LDPC) code, a code rate of the LDPCcode being 5/15 and a code length of the LDPC code being 16200 bits,wherein the plurality of groups are deinterleaved based on a followingequation:Yπ(j)=Xj for (0≤j<N _(group)), where Xj is a j-th group among theplurality of groups, Yj is a j-th group among the deinterleavedplurality of groups, Ngroup is a number of the plurality of groups andπ(j) denotes an interleaving order for the deinterleaving, and whereinthe π(j) is represented as follows: Order of deinterleaving π(j) (0 ≤ j< 45) Code j 0 1 2 3 4 5 6 7 Rate 23 24 25 26 27 28 29 30 5/15 π(j) 35 729 11 14 32 38 28 5 13 34 37 23 15 36 18 Order of deinterleaving π(j) (0≤ j < 45) Code j 8 9 10 11 12 13 14 15 Rate 31 32 33 34 35 36 37 38 5/15π(j) 20 17 25 39 19 4 1 12 42 16 33 31 27 22 3 6 Order of deinterleavingπ(j) (0 ≤ j < 45) Code j 16 17 18 19 20 21 22 Rate 39 40 41 42 43 445/15 π(j) 10 30 0 44 43 2 21 40 24 41 9 26
 8.


2. The broadcast signal receiving apparatus of claim 1, wherein each ofthe plurality of groups comprises 360 values.
 3. The broadcast signalreceiving apparatus of claim 1, wherein π(j) is determined based on atleast one of the code length, a modulation method and the code rate. 4.A broadcast signal transmitting apparatus comprising: an encoderconfigured to encode input bits to generate parity bits based on a lowdensity parity check (LDPC) code, a code rate of the LDPC code being5/15 and a code length of the LDPC code being 16200 bits; an interleaverconfigured to split a codeword comprising the input bits and the paritybits into a plurality of bit groups, interleave the plurality of bitgroups, and interleave bits of the interleaved plurality of bit groups;a mapper configured to map the interleaved bits to constellation pointsfor quadrature phase shift keying (QPSK) modulation; and a transmitterconfigured to transmit a broadcast signal which is generated based onthe constellation points, wherein the plurality of bit groups areinterleaved based on a following equation:Y _(j) =X _(π(j)) for (0≤j<N _(group)), where Xj is a j-th bit groupamong the plurality of bit groups, Yj is a j-th bit group among theinterleaved plurality of bit groups, Ngroup is a number of the pluralityof bit groups and π(j) denotes an interleaving order for theinterleaving, and wherein the π(j) is represented as follows: Order ofinterleaving π(j) (0 ≤ j < 45) Code j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 3637 38 39 40 41 42 43 44 5/15 π(j) 35 7 29 11 14 32 38 28 20 17 25 39 194 1 12 10 30 0 44 43 2 21 5 13 34 37 23 15 36 18 42 16 33 31 27 22 3 640 24 41 9 26
 8.


5. The broadcast signal transmitting apparatus of claim 4, wherein eachof the plurality of bit groups comprises 360 bits.